Parabolic Kazhdan-Lusztig polynomials and representation theory

Sun, 12/11/2017 - 14:00
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Abstract: 

The famous Kazhdan-Lusztig conjectures, formulated in the late 1970s and proved soon after independently by Beilinson-Bernstein and Brylinski-Kashiwara,

underscore a deep relationship between representation theory, combinatorics and geometry.
Recent progress in representation theory of the general linear group over p-adic fields led us to speculate a relationship between particular cases of parabolic Kazhdan-Lusztig polynomials
(which are certain alternating sums of ordinary ones) and ordinary ones. I will discuss what is known theoretically and some empirical results.

No prior familiarity with these concepts will be assumed.

Based on joint work with Alberto Minguez.