The spherical Hecke algebra and its Gelfand-Graev representation

Valentin Buciumas (KdV Institute and University of Amsterdam)

Wednesday 29th March, 2023 16:00-17:00 Maths 311B


The spherical Hecke algebra plays an important role in the study of unramified representation of p-adic groups. The Satake isomorphism, which relates it to the category of representations of the dual group, can be seen as a basic instance of local Langlands correspondence. In the first part of this talk, I will give a short introduction to the Satake isomorphism for the spherical Hecke algebra, and to the Gelfand-Graev representation, which contains information about unramified Whittaker functions. 

In the second part of this talk, I will explain similar results for metaplectic covers of p-adic groups. On the dual side, an interesting object appears: Lusztig's quantum group at a root of unity. This is joint work with Manish Patnaik.

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