Three approaches to representation theory of p-adic groups, Slava Naprienko (University of North Carolina at Chapel Hill) -- February 29th, 2024

This talk is about Spherical and Whittaker functions which are certain matrix coefficients of the principal series representation of p-adic groups. Already simplest values of these functions are quite non-trivial and interesting: Spherical functions produce the Hall-Littlewood polynomials and Whittaker functions produce the Schur polynomials.

I am going to talk about the refined version of these functions called Iwahori Spherical and Iwahori Whittaker functions which are certain non-symmetric components of the functions above. I show that there are three ways to approach these functions: through algebra of Demazure-like operators, through geometry of the affine flag varieties, and through combinatorics of integrable lattice models.

This work is based on arXiv:2110.10377 and arXiv:2211.15850 (joint with Daniel Bump).

The seminar co-organizers are Ian Cavey, Andrew Hardt, Shiliang Gao, Elizabeth Kelley, and Alexander Yong.