Algebras of Curvatrure Forms on Flag
Manifolds, Forests, Monomial Ideals, and Parking Functions
Monday, February 14, 2000
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.
Speaker's contact info: apost at math.berkeley.edu