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Publications of Victor Kac

  1. On a characteristic property of locally Euclidean spaces, Uspehi Mat. Nauk. 191 (1964), No. 4, 225—227.
  2. (with E. Vinberg) Quasi-homogeneous cones, Math. Zametiki 1 (1967), 347—354 (English translation: Math. Notes 1 (1967)).
  3. Simple graded Lie algebras of finite growth, Funkt. Analys y eĝo prilozh. 1 (1967), No. 4, 82—83 (English translation: Funct. Anal. Appl. 1 (1967), 328—329).
  4. Graded Lie algebras and symmetric spaces, Funkt. Analys y eĝo prilozh. 2 (1968), No. 2, 93—94 (English translation: Funct. Anal. Appl. 2 (1968), 183—184).
  5. Simple irreducible graded Lie algebras of finite growth, Iz vestija AN USSR (ser. Math.) 32 (1968), 1923—1967 (English translation: Math. of USSR-Izvestija 2 (1968), 1271—1311).
  6. Some properties of the contragredient Lie algebras, Trudy MIEM, No. 5, 1969, 48—60.
  7. An algebraic definition of compact Lie groups, Trudy MIEM, No. 5, 1969, 36—47.
  8. Automoprhisms of finite order of semi-simple Lie algebras, Funkt. analys y eĝo prilozh. 3 (1969), No. 3, 94—96 (English translation: Funct. Anal. Appl. 3 (1969), 252—254).
  9. On classifications of simple Lie algebras over fields of non-zero characteristics, Izvestija AN USSR (ser. Math.) 34 (1970), 381—404 (English translation: Math of USSR-Izvestija 4 (1970), 391—413).
  10. (with B. Weisfeiler) Exponentials in Lie algebras of characteristic $p$, Izvestija AN USSR (ser. Math.) 35 (1971), 762—788 (English translation: USSR-Izvestija 5 (1971), 777—803).
  11. (with B. Weisfeiler) On irreducible representations of Lie $p$-algebras, Funkt. analys y eĝo prilozh. 5 (1971), No. 2, 28—36 (English translation: Funct. Anal. Appl. 5 (1971), 111—117).
  12. Global Cartan pseudogroups and simple Lie algebras of characteristic $p$, Uspehi Math. Nauk. 26 (1971), No. 3, 199—200.
  13. On algebras related to quantum field theory, All-Union Algebraic Colloquium, Kishinev, 1971, 140—141.
  14. On irreducible representations of Lie algebras of classical type, Uspehi Math. Nauk. 27 (1972), No. 5, 237—238.
  15. Filtered Lie algebras of Cartan type, Uspehi Math. Nauk. 29 (1974), No. 3, 203—204.
  16. Infinite-dimensional Lie algebras and the Dedekind $\eta$-function, Funkt. analys y eĝo prilozh. 8 (1974), No. 1, 77—78 (English translation: Funct. Anal. Appl. 8 (1974), 68—70).
  17. A description of filtered Lie algebras whose associated graded Lie algebras are of Cartan type, Izvestija AN USSR (ser. Math.) 38 (1974), 800—834 (English translation: Math. of USSR-Izvestija 8 (1974), 801—835; letter to the editor, 40 (1976), No. 6).
  18. On the question of description of the orbit space of linear algebraic groups, Uspehi Math. Nauk. 30 (1975), No. 6, 173—174.
  19. Classification of simple Lie superalgebras, Funct. Anal. y ego Prilozh. 9 (1975), No. 3, 91—92; letter to the editor, 10 (1976), No. 2, 93 (English translation: Funct. Anal. Appl. 9 (1975), 263—265).
  20. (with B. Weisfeiler) Coadjoint action of a semi-simple algebraic group and the center of the enveloping algebra in characteristic $p$, Proc. Kon. Nederl. Akad., Series A 38 (1976), 136—151.
  21. (with V. Popov and E. Vinberg) Sur les groupes linear algebrique avec algebres d'invariants libre, C.R. Acad. Sci. Paris, 283 (1976), 875—878.
  22. A sketch of Lie superalgebra theory, Comm. Math. Physics 53 (1977), 31—64.
  23. Characters of typical representations of classical Lie superalgebras, Comm. in Algebra 5 , No. 8 (1977), 889—897.
  24. Classification of simple $Z$-graded Lie superalgebras and simple Jordan superalgebras, Comm. in Algebra 5 , No. 13 (1977), 1375—1400.
  25. Lie superalgebras, Advances in Math. 26 , No. 1 (1977), 8—96.
  26. Classification of simple algebraic supergroups, Uspehi Math. Nauk. 32 , No. 3 (1977), 214—215.
  27. Infinite-dimensional algebras, Dedkind's $\eta $-function, classical Möbius function and the very strange formula, Advances in Math. 30 (1978), 85—136.
  28. (with E. Vinberg) Spinors of 13-dimensional space, Advances in Math. 30 (1978), 137—155.
  29. Representations of classical Lie superalgebras, Lecture Notes in Math. 676 (1978), 597—626.
  30. Contravariant form for infinite dimensional Lie algebras and superalgebras, Lecture Notes in Physics 94 (1979), 441—445).
  31. (with D. Kazhdan) Structure of representations with highest weight of infinite dimensional Lie algebras, Advances in Math. 34 (1979), 97—108.
  32. Highest weight representations of infinite dimensional Lie algebras, Proceedings of ICM, Helsinki 1978 (1980), 299—304.
  33. Infinite root systems, representations of graphs and invariant theory, Inventiones Math. 56 (1980), 57—92.
  34. An elucidation of "Infinite dimensional algebras$\ldots$ and the very strange formula" $E^{(1)}_8 $ and the cube root of the modular invariant $j $, Advances in Math. 35 (1980), 264—273.
  35. On simplicity of certain infinite-dimensional Lie algebras, Bul. Amer. Math. Soc. 2 (1980) 311—314.
  36. Some remarks on nilpotent orbits, Journal of Algebra 64 (1980) 190—213.
  37. (with D. Peterson) Affine Lie algebras and Hecke modular forms, Bull. Amer. Math. Soc. 3 (1980) 1057—1061.
  38. A remark on the Conway-Norton conjecture about the "Monster" simple group, Proc. Nat'l. Acad. Sci. USA, 77 (1980) 5048—5049.
  39. (with I. Frenkel) Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980) 23—66.
  40. Some remarks on representations of quivers and infinite root systems, Lecture Notes in Math. 832 (1980), 311—327.
  41. (with D. Kazhdan, J. Lepowsky and R. Wilson) Realization of the basic representation of the Euclidean Lie algebras, Advances in Math. 42 (1981), 83—112.
  42. Simple Lie groups and the Legendre symbol, Lecture Notes in Math. 848 (1981), 110—124.
  43. (with D. Peterson) Spin and wedge representations of infinite dimensional Lie algebras and groups, Proc. Nat'l. Acad. Sci. USA 78 (1981), 3308—3312.
  44. (with O. Gabber) On defining relations of certain infinite-dimensional Lie algebras, Bull. Amer. Math. Soc. 5 (1981), 185—189.
  45. (with K. Watanabe) Finite linear groups whose ring of invariants is a complete intersection, Bull. Amer. Math. Soc. 6 (1982), 221—223.
  46. (with V. Deodhar and O. Gabber) Structure of some categories of representations of infinite dimensional Lie algebras, Advances in Math. 45 (1982), 92—116.
  47. Infinite root systems, representations of graphs and invariant theory II, Journal of Algebra 78 (1982), 141—162.
  48. Some problems on infinite dimensional Lie algebras and their representations, Lecture Notes in Math. 933 (1982), 117—126.
  49. (with D. Peterson) Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci. USA 80 (1983), 1778—1782.
  50. Montecatini lectures on invariant theory, Lecture Notes in Math. 996 (1983), 74—108.
  51. (with D. Peterson) Regular functions on certain infinite-dimensional groups, Arithmetic and Geometry (ed. M. Artin and J. Tate), Progress in Math. 36 , Birkhäuser, Boston, 141—166, 1983.
  52. Infinite-dimensional Lie algebras, Progress in Math. 44 , Birkhäuser, Boston, 1983.
  53. (with D. Peterson) Infinite dimensional Lie algebras, theta functions and modular forms, Advances in Math. 53 (1984), 125—264.
  54. (with D. Peterson) Unitary structure in representation of infinite-dimensional groups and a convexity theorem, Invent. Math. 76 (1984), 1—14.
  55. Laplace operators of infinite-dimensional Lie algebras and theta functions, Proc. Nat'l. Acad. Sci. USA 81 (1984), 645—647.
  56. (with J. Dadok) Polar representations, J. Algebra 92 (1985), 504—524.
  57. Infinite dimensional Lie algebras, second edition, Cambridge University Press, 1985.
  58. Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups, Invent. Math. 80 (1985), 69—79.
  59. (with H. Jakobsen) A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras, Lecture Notes in Physics 226 (1985), 1—20.
  60. Constructing groups associated to infinite-dimensional Lie algebras, Proceedings of the conference on Infinite-dimensional groups, Berkeley 1984, MSRI publ. #4, 1985, 167—216.
  61. (with D. Peterson), Defining relations of certain infinite-dimensional groups, Proceedings of the Cartan conference, Lyon 1984, Asterisque, 1985, Numero hors serie, 165—208.
  62. ( with D. Peterson) Generalized invariants of groups generated by reflections, in Proceedings of the Conference Giornate di Geometria, Rome 1984. Progress in Math. 60 , Birkhäuser, 1985, 231—250.
  63. (with D. Peterson) 112 Constructions of the basic representation of the loop group of $E_8 $, Proceedings of the conference "Anomalies, geometry, topology," Argonne, 1985. World Scientific, 1985, 276—298.
  64. (with I.T. Todorov) Superconformal current algebras and their unitary representations, Comm. Math. Physics 102 (1985), 337—347.
  65. (with M. Wakimoto) Unitarizable highest weight representations of the Virasoro, Neveu-Schwarz and Ramond algebras, in Proceedings of the Symposium on conformal groups and structures, Claustal, 1985. Lecture Notes in Physics 261 (1986), 345—372.
  66. (with D. Peterson), Lectures on the infinite wedge representation and the MKP hierarchy, Seminaire de Math. Superieures, Les Presses de L'Université de Montréal 102 (1986), 141—186.
  67. Highest weight representations of conformal current algebras, Symposium on Topological and Geometric methods in Field theory, Espoo, Finland, 1986. World Scientific (1986), 3—16.
  68. (with D. Peterson) On geometric invariant theory for infinite-dimensional groups, in Lecture Notes in Math. 1271 , 102—142, 1987.
  69. (with J. Van de Leur) Super boson-fermion correspondence, Ann. de L'Institute Fourier 37 (1987), 99—137.
  70. (with A. Raina) Bombay lectures on highest weight representations of infinite-dimenonal Lie algebras, World Scientific, 1987.
  71. (with M. Wakimoto) Modular and conformal invariance constraints in representation theory of affine algebras, Advances in Math. 70 (1988), 156—234.
  72. (with E. Arbarello, C. De Concini and C. Procesi) Moduli spaces and curves and representation theory, Comm. in Math. Phys. 117 (1988), 1—36.
  73. (with M. Niculescu-Sanielevici) Decomposition of representations of exceptional affine algebras with respect to conformal subalgebras, Phys. Rev. D 37 (1988), 2231—2237.
  74. (with M. Wakimoto) Modular invariant representations of infinite dimensional Lie algebras and superalgebras, Proc. Nat'l. Acad. Sci. USA 85 (1988), 4956—4960.
  75. (with R. Moody and M. Wakimoto) On $E_{10}$, Proceedings of the 1987 conference on differential-geometrical methods in physics, Kluwer, 1988, 102—128.
  76. (with H. Jakobsen) A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras II, J. Funct. Anal. 82 (1989), 69—90.
  77. (with M. Wakimoto) Exceptional hierarchies of soliton equations, Proceedings of Symposia in Pure Math. 49 (1989), 191—237.
  78. (with E. Arbarello and C. De Concini) The infinite wedge representation and the reciprocity law for algebraic curves, Proceedings of Symposia in Pure Math. 49 (1989), 171—190.
  79. (with C. De Concini and D. Kazhdan) Boson-fermion correspondence over $\mathbb {Z}$, in Infinite-dimensional Lie algebras and groups, Adv. Ser. Math. Phys. 7 (1989), 124—137.
  80. (with J. van de Leur) Super boson-fermion correspondence of type B, in Infinite dimensional Lie algebras and groups, Adv. Ser. Math. Phys. 7 , World Scientific, 369—406, 1989.
  81. (with J. van de Leur) On classification of superconformal algebras, in Strings 88, World Scientific, 77—106, 1989.
  82. (with M. Wakimoto) Classifications of modular invariant representations of affine algebras, in Infinite dimensional Lie algebras and groups, Adv. Ser. Math. Phys. 7 , World Scientific, 138—177, 1989.
  83. (with C. De Concini) Representation of quantum groups at roots of 1, Colloque Dixmier, 1990, Progress in Math. 92 , Birkhäuser, 1990, 471—506.
  84. Infinite dimensional Lie algebras, third edition, Cambridge University Press, 1990.
  85. (with M. Wakimoto) Branching functions for winding subalgebras and tensor products, Acta Applicandae Math. 21 (1990), 3—39.
  86. (with A.S. Schwarz) Geometric interpretation of partition function of 2D quantum gravity, Phys. Lett. B 257 (1991), 329—334.
  87. (with C. De Concini) Representations of quantum groups at roots of 1: reduction to the exceptional case, in Adv. Series in Math. Phys. 16A (1992), 141—150.
  88. Modular invariance in mathematics and physics, AMS Centennial Publications II, Mathematics into the 21st century, 1992, 337—350.
  89. (S.-P. Wang) On automorphisms of Kac-Moody algebras and groups, Advances in Math. 92 (1992), 129—195.
  90. (with C. De Concini and C. Procesi) Quantum coadjoint action, AMS Math. Journal 5 (1992), 151—190.
  91. (with E. Frenkel and M. Wakimoto) Characters and fusion rules for $W $-algebras via quantized Drinfeld-Sokolov reduction, Comm. in Math. Phys., 147 (1992), 295—328.
  92. (with C. De Concini and C. Procesi) Some remarkable degenerations of quantum groups, Comm. Math. Phys. 157 (1993), 405—427. hep-th/9308138
  93. (with J. van de Leur) The $n $-component $KP $ hierarchy and represen tation theory, in Important developments in soliton theory, pp. 302—343, eds. A.S. Fokas and V.E. Zakharov, Springer-Verlag, 1993.
  94. (with A. Radul) Quasifinite highest weight modules over the Lie algebra of differential operators on the circle, Comm. Math. Phys. 157 (1993), 429—457. hep-th/9308153
  95. (with M. Wakimoto) A construction of generalized spin models, in Perspectives in Math. Physics, Conference Proceedings, Vol. 3, International Press, 1994, 125—150.
  96. (with W. Wang) Vertex operator superalgebras and their representations, Contemporary Mathematics 175 (1994), 161—191. hep-th/9312065
  97. (with M. Wakimoto) Integrable highest weight modules over affine superalgebras and number theory, Progress in Math. 123 (1994), 415—456. hep-th/9407057
  98. (with C. De Concini and C. Procesi) Some quantum analogues of solvable Lie groups, Proceedings of the International Colloquium on Geometry and Analysis, Bombay 1992, Oxford University Press, 1995, 41—66. hep-th/9308138
  99. (with A. Radul) Poisson structure in restricted Lie algebras, The Gelfand Mathematical Seminars,1996-1999, Birkhause, Boston, 1999, 77—84.
  100. (with E. Frenkel, A. Radul and W. Wang) ${\mathcal W}_{1 + \infty} $ and ${\mathcal W} (gl_N) $ at central charge $N$, Comm. Math. Phys. 170 (1995) 337—358. hep-th/9405121
  101. (with S.-J. Kang) Trace formula for graded Lie algebras and monstrous moonshine, Canadian Math.Soc.conference proceedings 16 (1995),141-154.
  102. (with J. Beck) Finite-dimensional representations of quantum affine algebas at roots of 1, AMS Math. Journal 9 (1996),391-423. hep-th/9410189
  103. (with E. Medina) On the SKP hierarchy, Lett.Math.Phys. 37 (1996), 435-448.
  104. (with A. Radul) Representation theory of the vertex algebra \(W_{1 + \infty}\), Transformation groups 1 (1996), 41-70. hep-th/9512150
  105. (with I. Todorov) Affine orbifolds and RCFT extensions of \(W_{1 + \infty}\), Comm. Math.Phys., 190 (1997), 57-111. hep-th/9612078
  106. (with S.-J. Cheng) A new $N=6$ superconformal algebra, Comm. Math. Phys., 186 (1997), 219-231.
  107. Conformal superalgebras and transitive group actions on quadrics, Comm. Math. Phys., 186 (1997), 233-252. Erratum, 217(2001), 697-698.
  108. The idea of locality, in Physical applications and mathematical aspects of geometry, groups and algebras, H.-D. Doebner et al eds, World Sci., Singapore, 1997, pp 16-32. q-alg/9709008
  109. (with S.-J. Cheng) Conformal modules, Asian J. Math. 1 (1997), 181-193. Erratum, 2(1998),153-156. q-alg/9706030
  110. (with J. van de Leur) The geometry of spinors and the multicomponent $BKP$ and $DKP$ hierarchies, CRM Proceedings and Lecture Notes,14 (1998),159-202. solv-int/9706006
  111. (with S.-J. Cheng and M. Wakimoto) Extensions of conformal modules, in Topological field theory, primitive forms and related topics, Proceedings of Taniguchi and RIMS symposia, Progress in Math. 160 , Birkhäuser , 1998, pp 79-130. q-alg/9709019
  112. Formal distribution algebras and conformal algebras, in Proceedings of the 12th International Congress in Math. Physics, 1997, De Witt et al eds, International Press, Boston, 1999, pp 80-97. q-alg/9709027
  113. (with A. D'Andrea) Structure theory of finite conformal algebras, Selecta Matemathica, 4 (1998), 377-418.
  114. (with M. Golenishcheva-Kutuzova) $\Gamma$-conformal algebras, J. Math Physics 39 (1998), 2290-2305. q-alg/9709006
  115. (with C. Boyallian, J. Liberati and C. Yan) Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle, J. Math Physcis, 39 (1998), 2910—2928.
  116. (with W. Wang and C. Yan) Quasifinite representations of classical Lie subalgebras of $W_{1+ \infty}$, Advances in Math, 139 (1998), 56-140. QA/9801136
  117. Classification of infinite-dimensional simple linearly compact Lie superalgebras, Adv. in Math., 139 (1998), 1-55. ESI preprint no 406 ,1998.
  118. (with B. Bakalov and A. Voronov) Cohomology of conformal algebras, Comm. Math. Phys.200 (1999), 561-598. math.QA/9803022
  119. (with S.-J. Cheng) Generalized Spencer cohomology and filtered deformations of $\mathbb{Z}$-graded Lie superalgebras, Advances in Theor. and Math. Physics, 2 (1998), 1139-1180. math.RT/9805039
  120. (with S.-J. Cheng) Structure of some $\mathbb{Z}$-graded Lie superalgebras of vector fields, Transformation groups, 4 (1999), 219-272. Erratum, 9(2004), 399-400.
  121. (with A. Smilga) Vacuum structure in supersymmetric Yang-Mills theories with any gauge group, in: The many faces of the Superworld, Golfand memorial volume, M. Shifman, ed, World sci., 2000, pp 185-234 . hep-th/9902029
  122. (with A. Smilga) Normalized vacuum states in N=4 supersymmetric Yang-Mills quantum mechanics with any gauge group, Nuclear Physics B571 (2000),515-554. hep-th/9908096
  123. (with S.-J. Cheng and M. Wakimoto) Extensions of Neveu-Schwarz conformal modules, J. Math. Physics 41 (2000), 2271-2294.
  124. Classification of infinite-dimensional simple groups of supersymmetries and quantum field theory, Proceedings of the conference "Visions in Mathematics toward the year 2000", GAFA , Special volume (2000), 162-183. math.QA/9912235
  125. (with J. Liberati) Unitary quasifinite representations of $W_{\infty}$, Letters in Math. Phys.53 (2000), 11-27. math.QA/9910172
  126. (with C. Martinez and E. Zelmanov) Graded simple Jordan superalgebras of growth one, Memoirs of AMS 711, 2001, pp 1-140.
  127. (with M. Wakimoto) Integrable highest weight modules over affine superalgebras and Appell's function, Comm. Math. Phys. 215 (2001), 631-682. math-ph/0006007
  128. (with B. Bakalov and A. D'Andrea) Theory of finite pseudoalgebras, Advances in Math. 162 (2001), 1-140. math.QA/0007121
  129. (with J. Troost) The stability of vacua in two-dimensional gauge theory, Phys. Letters B501 (2001),313-318. hep-th/0010289
  130. A differential analog of a theorem of Chevalley, IMRN 13 (2001), 703-710. math.AG/0101210
  131. (with A. Rudakov) Representations of the exceptional Lie superalgebra E(3,6) I: Degeneracy conditions, Transformation groups 7 (2002), 67-86. math-ph/0012049
  132. (with A. Rudakov) Representations of the exceptional Lie superalgebra E(3,6) II: Four series of degenerate modules, Comm. Math. Phys. 222 (2001), 611-661. math-ph/0012050
  133. (with D. Fattori) Classification of finite simple Lie conformal superagebras, J. Algebra 258 (2002),23-59. math-ph/0106002
  134. (with P. Cheung) Quantom calculus, Springer Verlag, 2002
  135. (with A. Rudakov) Complexes of modules over exceptional Lie superalgebras E(3,8) and E(5,10), IMRN 19 (2002),1007-1025. math-ph/0112022
  136. (with A. De Sole) Subalgebras of $gc_N$ and Jacobi polynomials, Canadian Math. Bull. 45 (4)(2002),567-605. math-ph/0112028
  137. (with C. Boyallian and J. Liberati) On the classification of subalgebras of $Cend_N$ and $gc_N$, J. Algebra 260 (2002), 32-63. math-ph/0203022
  138. Classification of supersymmetries, ICM, Beijing 2002. math-ph/0302016
  139. (with B. Bakalov) Field algebras, IMRN, 2003, no 3, 123-159. math.QA/0204282
  140. (with C.Boyallian and J. Liberati) Finite growth representations of infinite Lie conformal algebras, J. Math. Phys. 44 (2003), 754-770. math.QA/0210161
  141. (with S.-S. Roan and M. Wakimoto) Quantum reduction for affine superalgebras. Comm. Math. Phys.241 (2003),307-342. math-ph/0302015
  142. (with J. van de Leur) The $n $-component $KP $ hierarchy and representation theory. J. Math. Phys. 44 (2003), 3245-3293.
  143. (with M. Wakimoto) Quantum reduction and representation theory of superconformal algebras. Advances in Math. 185 (2004), 400-458. math-ph/0304011. Corrigendum: Advances in Math. 193(2005),453-455.
  144. (with D. Fattori and A. Retakh) Structure theory of finite Lie conformal superalgebras, in "Lie theory and its applications to physics", eds. H.-D. Doebner and V.K. Dobrev, World Sci. 2004, pp 27-63. math.QA/0402211
  145. (with B. Bakalov) Twisted modules over lattice vertex algebras, in "Lie theory and its applications to physics", eds. H.-D. Doebner and V.K. Dobrev, World Sci. 2004, pp 3-26. math.QA/0402315
  146. (with S.-J. Cheng) Addendum: Generalized Spencer cohomology and filtered deformations of $\mathbb{Z}$-graded Lie superalgebras. Adv. Theor. Math. Phys. 8 (2004), 697-709.
  147. (with A. De Sole) On integral representations of q-gamma and q-beta functions. Rend. Mat. Acc. Lincei 9 (2005), 11-29. math.QA/0302032
  148. (with R. Longo and F. Xu) Solitons in affine and permutation orbifolds. Comm. Math. Phys. 253 (2005), 723-764. math.OA/0312512
  149. (with A. De Sole) Freely generated vertex algebras and non-linear Lie conformal algebras. Comm. Math. Phys. 254 (2005), 659-694. math-ph/0312042
  150. (with A.G. Elashvili) Classification of good gradings of simple Lie algebras, Amer. Math. Soc. Transl. (2) vol 213 (2005), 85-104. math-ph/0312030
  151. (with A. Rudakov) Representations of the exceptional Lie superalgebra E(3,6) III: Classification of singular vectors. J. Algebra Appl. 4 (2005), 15-57. math-ph/0310045
  152. (with M. Wakimoto) Quantum reduction in the twisted case. Progress in Math. 237, 2005, pp 85-126. math-ph/0404049
  153. (with B. Bakalov and A. D'Andrea) Irreducible modules over finite simple Lie pseudoalgebras I. Primitive pseudoalgebras of type W and S. Advances in Math.204 (2006),278-346. math.QA/0410213
  154. (with P. Cellini, P. Moseneder Frajria and P. Papi) Decomposition rules for conformal pairs associated to symmetric spaces and abelian ideals of $\mathbb{Z}_2$-graded Lie algebras. Advances in Math. 207 (2006), 156-204. math-ph/0506043
  155. (with C.Boyallian, J. Liberati and A. Rudakov) Representations of simple finite Lie conformal superalgebras of type $W$ and $S$. J. Math. Phys. 47 , 043513 (2006), 25pp. arXiv:1003.4416
  156. (with A. De Sole) Finite vs affine W-algebras. Japanese Journal of Math. 1 (2006), 137-261. math-ph/0511055
  157. (with N. Cantarini) Infinite-dimensional primitive linearly compact Lie superalgebras. Advances in Math.207 (2006), 328-419. math.QA/0511424
  158. (with N. Cantarini) Automorphisms and forms of simple infinite- dimensional linearly compact Lie superalgebras. Internat. J. of Geom. Methods in Phys. 3 , Nos. 5 and 6 (2006),1-23. math.QA/0601292
  159. (with B. Bakalov) Generalized vertex algebras, in "Lie theory and its applications to physics VI", eds.V.K. Dobrev et al, Heron Press, Sofia, 2006. math.QA/0602072
  160. (with R. Heluani) Supersymmetric vertex algebras. Comm. Math. Phys. 271 (2007), 103-178. math.QA/0603633
  161. (with M. Gorelik) On simplicity of vacuum modules. Advances in Math. 211 (2007), 621-677. math-ph/0606002
  162. (with N. Cantarini) Classification of simple linearly compact Jordan and generalized Poisson superalgebras. J. Algebra 313 (2007), 100-124. math.QA/0608390
  163. (with M. Gorelik) Characters of highest weight modules over affine Lie algebras are meromorphic functions. IMRN 2007, no 20, rnm079-25, 25pp. arXiv: 0704.2876
  164. (with P. Moseneder Frajria and P. Papi) Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting. Advances in Math. 217 (2008), 2485-2562. arXiv: 0704.3342
  165. (with R. Heluani) SUSY lattice vertex algebras. in "Lie theory and its applications to physics VII", eds.V.K. Dobrev et al, Heron Press, Sofia, 2008, pp 3-24. arXiv:0710.1587
  166. (with A. Retakh) Simple Jordan conformal superalgebras. J. Algebra Appl. 7 (2008), 517-533. arXiv:0801.0755
  167. (with M. Wakimoto) On rationality of W-algebras. Transformation groups 13 (2008), 671-713. arXiv:0711.2296
  168. (with P. Moseneder Frajria and P. Papi) On the kernel of the affine Dirac operator. Moscow Math. J. 8 (2008), 759-788. arXiv:0804.3495. Addendum. Moscow Math. J. 9 (2009).
  169. (with M. Lau and A. Pianzola) Differential conformal superalgebras and their forms. Advances in Math. 222 (2009),809-861. arXiv:0805.4243
  170. (with A.G. Elashvili and E.B. Vinberg) On exceptional nilpotents in semisimple Lie algebras. J. Lie Theory. 19 (2009), 371-390. arXiv:0812.1571
  171. (with A. De Sole) Lie conformal algebra cohomology and the variational complex. Comm. Math. Phys. 292 (2009), 667-719. arXiv:0812.4897
  172. (with M. Gorelik) On complete reducibility for infinite-dimensional Lie algebras. Advances in Math. 226 (2011), 1911-1972. arXiv:0905.0893
  173. (with A. Barakat and A. De Sole) Poisson vertex algebras in the theory of Hamiltonian equations. Japan. J. Math. 4 (2009), 141-252. arXiv:0907.1275
  174. (with N. Cantarini) Classification of linearly compact simple rigid superalgebras. IMRN 2010 , no 17, 3341-3393. arXiv:0909.3100
  175. (with N. Cantarini) Classification of simple linearly compact $n$-Lie superalgebras. Comm. Math. Phys. 298 (2010), 833-853. arXiv:0909.3284
  176. (with C. Boyallian and J. Liberati) Irreducible modules over simple Lie conformal superalgebras of type $K$, J. Math. Phys. 51 (2010)063507, 37 pp. arXiv:1003.4420
  177. (with B. Bakalov and A. D'Andrea) Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type K. Advances Math. 232 (2013), 188-237. arXiv:1003.6055
  178. (with A. De Sole and M. Wakimoto) On classification of Poisson vertex algebras. Transformation Groups 15 (2010), 883-907. arXiv:1004.5387
  179. (with A. De Sole and P.Hekmati) Calculus structure on the Lie conformal algebra complex. J. Math. Phys. 52 (2011), no 5, 053510, 35pp. arXiv:1007.3707
  180. (with N. Cantarini) Classification of linearly compact simple algebraic N=6 3-algebras. Transformation Groups 16 (2011),649-671. arXiv:1010.3599
  181. (with M. Gorelik, P. Moseneder Frajria and P. Papi) Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs. Japan. J. Math.7 (2012), 41-134. arXiv:1102.3785
  182. (with A. De Sole) The variational Poisson cohomology. Japan. J. Math. 8 (2013), 1-145. arXiv:1106.0082
  183. (with A. De Sole) Essential variational Poisson cohomology. Comm. Math. Phys. 313 (2012), 837-864. arXiv:1106.5882
  184. (with C. Boyallian and J. Liberati) Classification of finite irreducible modules over the Lie conformal superalgebra $CK_6$, Comm. Math. Phys. 317 (2013), 503-546. arXiv:1110.3972
  185. (with S. Carpentier and A. De Sole) Some algebraic properties of differential operators. J. Math. Phys. 53 (2012), no. 6. 063501. arXiv:1201.1992
  186. (with A.G. Elashvili and E.B. Vinberg) Cyclic elements in semisimple Lie algebras. Transformation Groups 18 (2013), 97-130. arXiv:1205.0515
  187. (with S. Carpentier and A. De Sole) Rational matrix pseudodifferential operators. Selecta Math. 20 (2014). no 2, 403-419 . arXiv:1206.4165
  188. (with A. De Sole and D. Valeri) Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Comm. Math. Phys. 323 (2013),663-711. arXiv:1207.6286
  189. (with P. Moseneder Frajria, P. Papi and F. Xu) Conformal embeddings and simple current extensions. IMRN 2015, no 14, 5229-5288. arXiv:1210.6602
  190. (with S. Carpentier and A. De Sole) Some remarks on non-commutative principal ideal rings. C.R. Math. Acad. Sci. Paris, 351 (2013), 5-8. arXiv:1305.0380
  191. (with A. De Sole) Non-local Poisson structures and applications to the theory of integrable systems. Jpn. J. Math. 8 (2013), 233-347. arXiv:1302.0148
  192. (with A. De Sole and R. Turhan) A new approach to the Lenard-Magri scheme of integrability. Comm. Math. Phys.330 (2014), 107-122. arXiv:1303.3438
  193. (with P. Moseneder Frajria and P. Papi) Dirac operators and the very strange formula for Lie superalgebras, in Advances in Lie superalgebras. Springer INDAM Series 7 , 2014, pp 121-147. arXiv:1305.5043
  194. (With A. De Sole and D. Valeri) Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents. Commun. Math. Phys. 331 (2014), 623-676. arXiv:1306.1684
  195. (with A. De Sole and D. Valeri) Dirac reduction for Poisson vertex algebras. Commun. Math. Phys. 331 (2014), 1155-1190. arXiv:1306.6589
  196. (with M. Wakimoto) Representations of affine superalgebras and mock theta functions. Transformation Groups 19 (2014), 383-455 . arXiv:1308.1261
  197. (with S. Carpentier and A. De Sole) Singular degree of a rational matrix pseudodifferential operator. IMRN 2015, no 13, 5162-5196. arXiv:1308.2647
  198. (with N. Cantarini) Algebraic vs physical N=6 3-algebras. J. Math. Phys. 55 (2014), 011704. arXiv:1309.7746
  199. (with A. De Sole and D. Valeri) Adler-Gelfand-Dickey approach to classical W-algebras via the theory of Poisson vertex algebras. IMRN 2015, no 21, 11186-11235. arXiv:1401.2082
  200. (with A. De Sole and D. Valeri) Integrability of Dirac reduced bi-Hamiltonoan equations, in Trends in Contemporary Math, Springer INDAM Series 8 , 2014, pp 13-32. arXiv:1401.6006
  201. (with M. Wakimoto) Representations of affine superalgebras and mock theta functions II. Advances in Math.300 (2016), 17-70. arXiv:1402.0727
  202. (with A. De Sole and D. Valeri) Structure of classical (finite and affine) W-algebras. J. Eur. Math. Soc. 18 (2016), 1873-1908. arXiv:1404.0715
  203. (with A. De Sole and R. Turhan) On integrability of some bi-Hamiltonian two field systems of PDE. J. Math. Phys. 56 (2015), no 5, 051503. arXiv:1405.1349
  204. (with M. Gorelik) Characters of (relatively) integrable modules over affine Lie superalgebras. Jpn. J. Math. 10 (2015), no 2, 135-235. arXiv:1406.6860
  205. (with A. De Sole and D. Valeri) Erratum to: Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents, Commun. Math. Phys. 333 (2015), no 3, 1617-1619.
  206. (with A. De Sole and D. Valeri) Double Poisson vertex algebras and non-commutative Hamiltonian equations. Advances in Math. 281 (2015), 1025-1099. arXiv:1410.3325
  207. (with M. Wakimoto) Representations of affine superalgebras and mock theta functions III. Izvestija RAN Ser Mat. 80 (2016), no 4, 65-122. arXiv:1505.01047
  208. (with A. De Sole and D. Valeri) A new scheme of integrability for (bi) Hamiltonian PDE. Comm. Math. Phys. 347 (2016), no 2, 449-488. arXiv:1508.02549
  209. (with D. Adamovic, P. Moseneder Frajria, P. Papi and O. Perse) Finite vs infinite decompositions in conformal embeddings. Comm. Math. Phys. 348 (2016), no 2, 345-473. arXiv:1509.06512.
  210. (with A. De Sole and D. Valeri) Classical affine $W$-algebras for $gl_N$ and associated integrable Hamiltonian hierarchies. Comm. Math. Phys. 348 (2016), no 1, 265-319. arXiv:1509.06878.
  211. (with M. Wakimoto) A characterization of modified mock theta functions. Transformation Groups 22 (2017) arXiv:1510.05683.
  212. (with N. Cantarini) Classification of linearly compact simple Nambu-Poisson algebras. J. Math. Phys. 57 (2016), no 5, 051701. arXiv:1511.04957.
  213. Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE, in Perspecives in Lie theory. Springer INDAM Ser. 19 (2017), 3-72. arXiv:1512.00821.
  214. (with D. Adamovic, P. Moseneder Frajria, P. Papi and O. Perse) Conformal embeddings of affine vertex algebras in minimal W-algebras I: structural results. J. Algebra (2017) arXiv:1602.04687.
  215. (with D. Adamovic, P. Moseneder Frajria, P. Papi and O. Perse) Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions. Japan. J. Math. (2017), -. arXiv:1604.00893
  216. (with A. De Sole and D. Valeri) Finite $W$-algebras for $gl_N$. Advances in Math. (2017) arXiv:1605.02898
  217. (with M. Wakimoto) A remark on boundary level admissible representations, C.R. Math. Acad. Sci. Paris, 355 (2017), no 2, 128-132. arXiv:1612.07423
  218. (with M. Wakimoto) Representations of superconformal algebras and mock theta functions, Proc. Moscow Math. Soc. 78 (2017), no 1, 17-88. arXiv:1701.03344
  219. (with D. Adamovic, P. Moseneder Frajria, P. Papi and O. Perse) On classification of non-equal rank affine conformal embeddings and applications. Japan. J. Math. (2017) arXiv:1702.06089
  220. (with A. De Sole and D. Valeri) Classical affine $W$-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras. arXiv:1705.10103
  221. (with M. Wakimoto) On characters of irreducible highest weight modules of negative integer level over affine Lie algebras. arXiv:1706.08387
  222. (with A. De Sole and D. Valeri) A Lax type operator for quantum finite $W$-algebras. arXiv:1707.03669
  223. (with J. van de Leur) Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions. arXiv:1801.02845
  224. (with D. Adamovic, P. Moseneder Frajria, P. Papi and O. Perse) An application of collapsing levels to representation theory of affine vertex algebras. arXiv:1801.09880
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