EVENT DETAILS AND ABSTRACT

Title: Kazhdan-Lusztig polynomials and canonical basis
Speaker: Professor Alexander Kirillov Jr.
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

We show that the Kazhdan--Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group $S_n$ coincide with the coefficients of the canonical basis in $n$th tensor power of the fundamental representation of the quantum group $U_q (sl_k)$. We also use known results about canonical bases for $U_q(sl_2)$ to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmanians), due to Lascoux-Schutzenberger and Zelevinsky.

This is joint work with Igor Frenkel and M. Khovanov.