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Hecke eigen-functions for curves over local non-archimedian fields

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Alexander Braverman
University of Toronto
Tue, 23/04/2024 - 16:30 - 17:30
MPIM Lecture Hall
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Extra talk

We give a survey of some recent constrictions and results concerning Hecke operators for the moduli space of G-bundles on a smooth projective curve X defined over a local non-archimedian field F (possibly with level structures). These operators are somewhat analogous to the usual Hecke operators in the case when F is a finite field but describing their common eigen-values is a much more difficult task. We'll discuss on what space the Hecke operators act, formulate some general conjectures about eigen-functions and consider some examples. In the end (if time permits) I would like to discuss the example when X is of genus 0, and we study bundles with triviliazation at two points. This example is closely related to  the usual representation theory of G(F). 

The talk is based on joint works (partly in progress) with P.Etingof, D.Kazhdan and A Polishchuk.
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