Parabolic Kazhdan-Lusztig polynomials and representation theory
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.