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表現論セミナー Hecke algebras, Whittaker functions and quantum groups（Valentin Buciumas氏）

2024年11月18日

2024年11月26日開催

2024年11月26日 15時30分～ 2024年11月26日 17時00分

理学部3-413

Valentin Buciumas氏 (Pohang University of Science and Technology)

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 as well as some connections

to algebraic combinatorics. In particular I will try to explain how one can use ideas

from the theory of symmetric functions to study both p-adic groups and their quantum counterparts.

(対面のみ開催)