[GAP] Valentin Buciumas - Hecke algebras, Whittaker functions and quantum groups

Описание: Geometry, Algebra and Physics Seminar at KIAS
https://sites.google.com/view/gapkias

hosted by Hyun Kyu Kim, at KIAS (Korea Institute for Advanced Study)
https://www.kias.re.kr/

supported by Korea Institute for Advanced Study

2024.Apr.25.
speaker : Valentin Buciumas (POSTECH, Korea)
title : Hecke algebras, Whittaker functions and quantum groups
abstract:
I will give a brief overview of the Satake isomorphism and the Casselman-Shalika formula, which are basic tools in the representation theory of p-adic groups. These two results essentially state that the spherical Hecke algebra and the spherical Whittaker functions on a p-adic group can be understood in terms of the representation theory of the dual group.
When passing from p-adic groups to their metaplectic covers, it was conjectured by Gaitsgory and Lurie (recently proved in different settings by Campbell-Dhillon-Raskin and Buciumas-Patnaik) that the dual group gets replaced by a certain quantum group at a root of unity. I will try to explain the conjecture of Gaitsgory-Lurie and if time permits some of the ideas of the proof in the algebraic setting, as well as some interactions to combinatorics and number theory.