Algebras of Curvatrure Forms on Flag Manifolds, Forests, Monomial Ideals, and Parking Functions

Alexander Postnikov

(UC Berkeley)

Monday, February 14, 2000
3:00 pm
939 Evans Hall


We lift the cohomology ring of the flag manifold F_n to the level of differential forms. The main object is the algebra generated by the curvature 2-forms of line bundles over F_n. Its dimension equals to the number of forests on n labelled vertices. This construction leads to general definition of a certain class of algebras associated with monomial ideals. The bases in these algebras are labelled by generalized parking functions. The talk is based on a joint work with Boris and Mikhail Shapiro.

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