September 9: Shuai Wang

Title: Non-recursive formula for Kazhdan-Lusztig polynomials for finite and affine G/P

Abstract:

Brenti proves a non-recursive formula for the Kazhdan-Lusztig polynomials of Coxeter groups by combinatorial methods. In the case of the Weyl group of a split group over a finite field, a geometric interpretation of the formula is given by Sophie Morel via the "weight-truncation" theory of perverse sheaves developed by her. With suitable modifications of Morel's proof, we generalize the geometric interpretation to the case of finite and affine partial flag varieties. We also demonstrate the result for sl_3, sl_4 and affine sl_2.