Geometry/Physics Seminar

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

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.

Date: Thursday, November 13, 1997
Time: 4:10pm
Where: Lunt 103
Contact Person: Prof. Ezra Getzler
Contact email: getzler@math.nwu.edu
Contact Phone: 847-467-1695
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