数学研究所

学术报告

表示论研讨班

Speaker: Valentin Buciumas(Pohang university of science and technology)

Inviter: 聂思安 研究员

Language: English

Title: A geometric Casselman-Shalika formula for metaplectic covers of p-adic groups 

Time&Venue: 2025年4月3日（星期四） 14:30-16:30 & zoom：843 4053 1910

Abstract: The space of unramified Whittaker functions on the metaplectic cover of a p-adic group G has been studied for some time, influenced especially by the theory of multiple Dirichlet series, with several combinatorial formulas known about values of such functions, none of which involve the dual group.

In this talk, I'll explain how to describe this space in terms of the quantum group at a root of unity attached to the dual group of G, as conjectured by Gaitsgory-Lurie and in a refined form by Lysenko. The main tool we use is a novel description of the construction of certain Fock spaces that model the representation theory of the quantum group at a root of unity in terms of metaplectic Demazure-Lusztig operators. This allows us to develop a Gauss sum twisted Kazhdan-Lusztig combinatorics for the Whittaker space and to give certain combinatorial formulas of interest for the action of spherical Hecke algebra on it.

This is joint work with Manish Patnaik.