Algebras of Chern forms on flag manifolds and forests

Alexander Postnikov (MIT)

Room 2-338

4:15 p.m., Wednesday, February 11, 1998

Abstract: The algebra generated by the Chern forms of standard line bundles over the flag manifold Fl_n is a natural extension of the cohomology ring of Fl_n. We show that the dimension of this algebra is equal to the number of forests on n labelled vertices. We present an explicit construction for a monomial basis. More generally, the results naturally extend to a wider class of algebras, whose bases are labelled by generalized parking functions. This is a joint work with Boris Shapiro and Mikhail Shapiro.