January 30, 1997
Jiang-Hua Lu, University of Arizona
"Poisson goemetry and the Schubert calculus"
Abstract:
The theory of quantum groups gives rise to various Poisson structures
on semi-simple Lie groups and their homogeneous spaces. In this talk,
we make connections between these Poisson structures and a series of
theorems of Kostant in the 60's on Lie algebra cohomology. In particular,
we interpret Kostant's harmonic forms on the flag manifold $G/B$ in terms
of moment maps and Liouville volume forms coming from the Bruhat Poisson
structure on the flag manifold.