BERTRAM KOSTANT
 

I am Professor Emeritus at the MIT department of Mathematics.
My office number is 2-282, my phone number is (617)253-4998,
and my email address is kostant@math.mit.edu.


EDUCATION

1941-45 New York City Public Schools
1945 Graduated from Peter Stuyvesant High School
1950 B.S. Purdue University
1951 M.S. Mathematics, University of Chicago
1954 Ph.D. Mathematics, University of Chicago
 

MATHEMATICAL CAREER

1954-56 Institute of Advanced Study
1955-56 Higgins Lecturer at Princeton University
1956-59 Assistant Professor, University of California, Berkeley
1961-62 Associate Professor, University of California, Berkeley
1962 Professor, Berkeley
1962 Professor, MIT
1993 Professor Emeritus, MIT
 

SPECIAL FESTSCHRIFT LECTURER

1977 Andre Lichnerowicz Festschrift at Ecole Polytechnique in Paris
1980 Irving Segal Festschrift at MIT
1985 George Mackey Festschrift at MSRI, Berkeley
1987 Hommage to Elie Cartan, Lyons, France
1989 Jacques Dixmier Festschrift, Paris
1990 Jean-Marie Souriau Festschrift, Marseilles
1993 John Coleman Festschrift, Kingston, Ontario
1993 Israel M. Gelfand Festschrift, New Bruswick, NJ
 

FESTSCHRIFT VOLUME

Lie Theory and Geometry, In Honor of Bertram Kostant, Progress in Mathematics, 123, Birkhauser, Boston, 1994.
 

PAPERS OF BERTRAM KOSTANT
  1. Holonomy and the Lie Algebra of Infinitesimal Motions of a Riemannian Manifold, Trans. Amer. Math. Soc., 80, (1955), 528-542.

    2.  
  2. On the Conjugacy of Real Cartan Subalgebras I, Proc. Nat. Acad. of Sci., 41, (1955), No. 11, 967-970.

    3.  
  3. On the Conjugacy of Real Cartan Subalgebras II, Univ. of Chicago preprint, (1955), 1-9.

    4.  
  4. On Invariant Skew Tensors, Proc. Nat. Acad. of Sci., 42, (1956), No. 3, 148-151.

    5.  
  5. On Differential Geometry and Homogeneous Spaces I, Proc. Nat. Acad. Sci., 42, (1956), 258-261.

    6.  
  6. On Differential Geometry and Homogeneous Spaces II, Proc. Nat. Acad. Sci., 42, (1956), 354-357.

    7.  
  7. On Holonomy and Homogeneous Spaces, Nagoya Math. Jour., 12, (1957), 31-54.

    8.  
  8. A Theorem of Frobenius, A Theorem of Amitsur-Levitski and Cohomology Theory, J. of Math. and Mech., 7, (1958), No. 2, 237-264.

    9.  
  9. A Characterization of the Classical Groups, Duke Math. Jour., 25, (1958), No. 1, 107-124.

    10.  
  10. A Formula for the Multiplicity of a Weight, Trans. Amer. Math. Soc., 93, (1959), No. 1, 53-73.

    11.  
  11. The Three Dimensional Sub-Group and the Betti Numbers of a Complex Simple Lie Group, Amer. Jour. of Math., 81, (1959), 973-1032.

    12.  
  12. A Characterization of Invariant Affine Connections, Nagoya Math. Jour., 16, (1960), 35-50.

    13.  
  13. Lie Algebra Cohomology and the Generalized Borel-Weil Theorem, Ann. of Math., 74, (1961), No. 2, 329-387.

    14.  
  14. (with G. Hochschild and A. Rosenberg), Differential Forms on Regular Affine Algebras, Trans. Amer. Math. Soc., 102 , (1962), No. 3, 383-408.

    15.  
  15. (with G. Hochschild), Differential Forms and Lie Algebra Cohomology for Algebraic Linear Groups, Illinois Jour. of Math., 6, (1962), 264-281.

    16.  
  16. Lie Group Representations on Polynomial Rings, Bull. Amer. Math. Soc., 69, (1963), No. 1, 518-526.

    17.  
  17. Lie Group Representations on Polynomial Rings, Amer. J. Math., 85, (1963), 327-404.

    18.  
  18. Lie Algebra Cohomology and Generalized Schubert Cells, Ann. of Math., 77, (1963), No. 1, 72-144.

    19.  
  19. Eigenvalues of a Laplacian and Commutative Lie Subalgebras, Topology, 13, (1965), 147-159.

    20.  
  20. Orbits, Symplectic Structures and Representation Theory, Proc. of U.S.-Japan Seminar in Differential Geometry, Kyoto, Japan (1965), 71.

    21.  
  21. Groups Over Z, Proc. Symposia in Pure Math., 9, (1966), 90-98.

    22.  
  22. (with L. Auslander), Quantization and Representations of Solvable Lie Groups, Bull. Amer. Math. Soc., 73, (1967), No. 5, 692-695.

    23.  
  23. Irreducibility of Principal Series and Existence and Irreducibility of the Complementary Series, Bowdoin College Conf. on Algebraic Groups, Notes by Roger Richardson, 1968, 1-41.

    24.  
  24. (with Stephen Rallis), Orbits Associated with Symmetric Spaces, Bull. Amer. Math. Soc., 75, (1969), 879-883.

    25.  
  25. (with Stephen Rallis), Representations Associated with Symmetric Spaces, Bull. Amer. Math. Soc., 75, (1969), 884-888.

    26.  
  26. On the Existence and Irreducibility of Certain Series of Representations, Invited Address, Bull. Amer. Math. Soc., 75, (1969), 627-642.

    27.  
  27. On Certain Unitary Representations which arise from a Quantization Theory, Lecture Notes in Math., Battelle Seattle Rencontres, Springer Verlag, 6, (1970), 237-254.

    28.  
  28. Orbits and Quantization Theory, Proc. Int. Congress of Mathematicians, Nice, (1970), 395-400.

    29.  
  29. Quantization and Unitary Representations, Lecture Notes in Math. 170, Springer-Verlag, (1970), 87-207.

    30.  
  30. (with Stephen Rallis), Orbits and Representations Associated with Symmetric Spaces, Amer. Jour. of Math., 93, (1971), 753-809.

    31.  
  31. (with L. Auslander), Polarization and Unitary Representations of Solvable Lie Groups, Inventiones Math., 14, (1971), 255-354.

    32.  
  32. Line Bundles and the Prequantized Schroedinger Equation, Coll. Group Theoretical Methods in Physics, Centre de Physique Theorique, Marseille, (1972), 81-85.

    33.  
  33. On Convexity, the Weyl Group and the Iwasawa Decomposition, Ann. Sci. Ecole Norm. Sup., 6, (1973), No. 4, 413- 455.

    34.  
  34. Symplectic Spinors, Rome Symposia, XIV, (1974), 139-152.

    35.  
  35. Verma Modules and the Existence of Quasi-Invariant Differential Operators, Lecture Notes in Math. 466, Springer Verlag, (1974), 101-129.

    36.  
  36. On the Existence and Irreducibility of Certain Series of Representations, Lie Groups and Their Representations, edited by I. M. Gelfand, Summer School Conf. Budapest, (1971), Halsted and Wiley Press (1975), 231-331.

    37.  
  37. On The Tensor Product of a Finite and an Infinite Dimensional Representation, J. Funct. Anal., 20, (1975), No. 4, 257-285.

    38.  
  38. On the Definition of Quantization, Geometrie Symplectique et Physique Mathematique, Coll. CNRS, No. 237, Paris, (1975), 187-210.

    39.  
  39. (with D. Sullivan), The Euler Characteristic of an Affine Space Form is Zero, Bull. Amer. Math. Soc., 81, (1975), No. 5, 937-938.

    40.  
  40. On MacDonald's tex2html_wrap_inline194 - Function Formula, the Laplacian and Generalized Exponents, Adv. in Math., 20, (1976), No. 2, 179-212.

    41.  
  41. (with J. Tirao) On the Structure of Certain Subalgebras of a Universal Enveloping Algebra, Trans. Amer. Math. Soc., 218, (1976), 133-154.

    42.  
  42. Graded Manifolds, Graded Lie Theory, and Prequantization, Lecture Notes in Math. 570, Springer-Verlag, (1977), 177-306.

    43.  
  43. Quantization and Representation Theory, Proc. Oxford Conference on Group Theory and Physics, Oxford, (1977), 287-316.

    44.  
  44. Harmonic Analysis on Graded (or Super) Lie Groups, Group Theoretical Methods in Physics, Sixth International Colloquium, Lecture Notes in Physics, (1979), 47-50.

    45.  
  45. On Whittaker Vectors and Representation Theory, Inventiones Math., 48, (1978), 101-184.

    46.  
  46. (with D. Kazhdan and S. Sternberg), Hamiltonian Group Actions and Dynamical Systems of Calogero Type, Communications Pure and Applied Math., 31, (1978), No. 4, 483-507.

    47.  
  47. The Solution to a Generalized Toda Lattice and Representation Theory, Adv. in Math., 34, (1979), 195-338.

    48.  
  48. Poisson Commutativity and Generalized Periodic Toda Lattice, Differential Geometric Methods in Math. Physics, Lecture Notes in Mathematics 905, Springer Verlag, (1980), 12-28.

    49.  
  49. (with S. Sternberg) Symplectic Projective Orbits, New Directions in Applied Mathematics, Springer Verlag, (1980), 81-84.

    50.  
  50. A Lie Algebra Generalization of the Amitsur-Levitski Theorem, Adv. in Math., 40, (1981), No. 2, 155-175.

    51.  
  51. Coadjoint Orbits and a New Symbol Calculus for Line Bundles, Conf. on Diff. and Geometric Methods in Theoretical Physics, Trieste, (1980), World Scientific Publishing, (1981), 66-68.

    52.  
  52. The Coxeter Element and the Structure of the Exceptional Lie Groups, Coll. Lectures of the AMS, (1983), AMS Notes.

    53.  
  53. The McKay Correspondence, the Coxeter Element and Representation Theory, Societe Math. de France, Asterisque, hors series, (1985), 209-255.

    54.  
  54. (with Shrawan Kumar), The Nil Hecke Ring and Cohomology of G/P for a Kac-Moody Group G, Adv. in Math., 62, (1986), 187-237.

    55.  
  55. (with S. Sternberg), Symplectic Reduction, BRS Cohomology and Infinite Dimensional Clifford Algebras, Annals of Physics, 176, (1987), 49-113.

    56.  
  56. (with S. Kumar), T-Equivariant K-Theory of Generalized Flag Varieties, Journal of Differential Geometry, 32, (1990), 549-603.

    57.  
  57. (with V. Guillemin and S. Sternberg), Douglas's Solution to the Plateau Problem, Proc. Nat. Acad. Sciences, 85, (1988), 3277-3278.

    58.  
  58. The Principle of Triality and a Distinguished Unitary Representation of S0(4,4), Differential Geometrical Methods in Theoretical Physics, edited by K. Bleuler and M. Werner, Kluwer Academic Publishers, (1988), 65-108.

    59.  
  59. (with S. Sternberg), The Schwartzian Derivative and the conformal geometry of the Lorentz Hyperboloid, Quantum Theories and Geometry, edited by M. Cahen and M. Flato, Kluwer Academic Publishers (1988), 113-125.

    60.  
  60. A Formula of Gauss-Kummer and the Trace of Certain Intertwining Operators, The Orbit Method in Representation Theory, edited by Duflo, Pedersen and Vergne, Birkhauser, (1990), 99-134.

    61.  
  61. A Tale of Two Conjugacy Classes, preprint, 1990.

    62.  
  62. The Vanishing of Scalar Curvature and the Minimal Unitary Representation of SO(4,4), Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Edited by Connes et al, PM 92, Birkhauser-Boston, (1990), 85-124.

    63.  
  63. (with Shrawan Kumar), A Geometric Realization of Minimal K-Types of Harish-Chandra Modules, Kazhdan-Lusztig Theory and related Topics, Contemporary Math., edited by V.V. Deodhar, 139, (1992), Providence.

    64.  
  64. (with Siddhartha Sahi), The Capelli Identity, Tube Domains and a Generalized Laplace Transform, Advances in Math., 87, (1990), 71-92.

    65.  
  65. (with Ranee Brylinski), The Variety of all Invariant Symplectic Structures on a Homogeneous Space, Symplectic Geometry and Mathematical Physics, PM, 99, Edited by Donato et al. Birkhauser-Boston, (1991), 80-113.

    66.  
  66. (with Ranee Brylinski), Nilpotent Orbits, Normality and Hamiltonian Group Actions, Bull. Amer. Math. Soc., 26, (1992), 269-275.

    67.  
  67. (with Siddhartha Sahi), Jordan Algebras and Capelli Identities, Inventiones Math., 112, (1993), 657-664.

    68.  
  68. (with Ranee Brylinski), Nilpotent Orbits, Normality and Hamiltonian Group Actions 2, Journ. Amer. Math. Soc., 7, (1994), 269-298.

    69.  
  69. (with Ranee Brylinski), Minimal representations of tex2html_wrap_inline200 , tex2html_wrap_inline202 and tex2html_wrap_inline204 , Unitarity and the Generalized Capelli Identity, Proc. Nat. Acad Sci., 91, (1994), 2469-2472.

    70.  
  70. (with F. Chung and S. Sternberg), Groups and the Buckyball, Lie Theory and Geometry: In Honor of Bertram Kostant, edited by J.-L. Brylinski et al., PM, 123, (1994), Birkhauser, Boston, 97-126.

    71.  
  71. (with Ranee Brylinski), Differential Operators on Conical Lagrangian Manifolds, Lie Theory and Geometry: In Honor of Bertram Kostant, edited by J.-L. Brylinski et al., PM, 123, Birkhauser, Boston, (1994), 65-96.

    72.  
  72. (with Ranee Brylinski), Minimal Representations, Geometric Quantization, and Unitarity, Proc. Nat. Acad. Sci., 91, (1994), 6026-6029.

    73.  
  73. Structure of the Truncated Icosahedron (such as Fullerene or Viral Coatings) and a 60-element Conjugacy Class in PSl(2,11), Proc. Nat. Acad. Sci., 91, (1994), 11714-11717.

    74.  
  74. Immanant Inequalities and 0-weight Spaces, Journ. Amer. Math. Soc., 8, (1995), 181-186.

    75.  
  75. (with Ranee Brylinski), Lagrangian Models of Minimal Representations of tex2html_wrap_inline200 , tex2html_wrap_inline202 and tex2html_wrap_inline204 , Functional Analysis on the Eve of the 21st Century: In Honor of I. M. Gelfand, PM, 131, Birkhauser, Boston, (1995), 13-63.

    76.  
  76. Structure of the Truncated Icosahedron (e.g. Fullerene or C60) and a 60-element Conjugacy Class in PSl(2,11), Selecta Mathematica, New Series, 1, (1995), Birkhauser, 163-195.

    77.  
  77. The Graph of the Truncated Icosahedron and the Last Letter of Galois, Notices of the American Math. Society, Sept., (1995), 959-968.

    78.  
  78. Flag Manifold Quantum Cohomology, the Toda Lattice, and the Representation with Highest Weight tex2html_wrap_inline212 , Selecta Mathematica, New Series, 2, (1996), 43-91.

    79.  
  79. Clifford Algebra Analogue of the Hopf-Koszul-Samelson Theorem, the tex2html_wrap_inline212 - Decomposition,tex2html_wrap_inline216 , and the tex2html_wrap_inline218 - Module Structure oftex2html_wrap_inline220 , Adv. in Math., 125, (1997), 275-350.

    80.  
  80. Quantum Cohomology of the Flag Manifold as an Algebra of Rational Functions on a Unipotent Algebraic Group, Deformation Theory and Symplectic Geometry, Edited by D. Sternheimer et al, Kluwer, (1997), 157-175.

    81.  
  81. The Set of Abelian Ideals of a Borel Subalgebra, Cartan Decompositions, and Discrete Series Representations, IMRN, 5, (1998), 225-252.

    82.  
  82. (with B. Gross, P. Raymond and S. Sternberg) The Weyl character formula, the half-spin representations, and equal rank subgroups, Proc. Nat. Acad. Sci., 95, (1998), 8441-8442.

    83.  
  83. A Cubic Dirac Operator and the Emergence of Euler Number Multiplets of Representations for Equal Rank Subgroups, Duke Math Journal, 100, (1999), No.3, 447-501.

    84.  
  84. On tex2html_wrap_inline220 for a semisimple Lie algebra tex2html_wrap_inline218 , as an equivariant module over the symmetric algebra tex2html_wrap_inline226 , Advanced Studies in Pure Mathematics, 26, Analysis on Homogeneous Spaces and Representations of Lie Groups, (2000), 127-142.

    85.  
  85. A Generalization of the Bott-Borel-Weil Theorem, (to appear) Proceedings of the 1999 Dijon conference in memory of Moshe Flato, Edited by D. Sternheimer, Kluwer 2000.

    86.  
  86. On Laguerre Polynomials, Bessel Functions, Hankel Transform and a Series in the Unitary Dual of the Simply-Connected Covering Group of Sl(2,R), submitted to the Journal of Representation Theory.

    87.  
  87. On Dale Peterson's tex2html_wrap_inline228 Abelian Ideal Theorem, Symmetric spaces, Discrete Series, and Euler Number Multiplets of Representations, In Preparation.

 

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