Mathematics Colloquia and Seminars
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Strong Macdonald theorems and Kahler geometry of affine flag varietiesAlgebra & Discrete Mathematics
|Speaker: ||William Slofstra, UC Davis|
|Location: ||1147 MSB|
|Start time: ||Mon, Nov 26 2012, 4:10PM|
The Macdonald constant term identity for the root system of a
semisimple Lie algebra L can be proved by calculating the Lie algebra
cohomology of L[z,s], where z is an ordinary variable and s is an odd variable.
This calculation was completed by Fishel, Grojnowski, and Teleman using ideas
from the Kahler geometry of the loop Grassmannian. I will explain how to extend
this calculation to an arbitrary affine flag variety, leading to strong
Macdonald theorems for parahoric subalgebras of any affine Kac-Moody algebra.
As applications, we will get a proof of the affine constant term identities,
and also a proof that the affine Kostka-Foulkes polynomials have positive