Vol. 319, No. 2, 2022

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A Hecke algebra isomorphism over close local fields

Radhika Ganapathy

Vol. 319 (2022), No. 2, 307–332
Abstract

Let G be a split connected reductive group over . Let F be a nonarchimedean local field. With Km := Ker (G(𝔒F) G(𝔒F𝔭Fm)), Kazhdan proved that for a field F sufficiently close local field to F, the Hecke algebras (G(F),Km) and (G(F),Km) are isomorphic, where Km denotes the corresponding object over F. We generalize this result to general connected reductive groups.

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Keywords
Hecke algebra, close local fields
Mathematical Subject Classification
Primary: 22E50
Secondary: 11F70
Milestones
Received: 22 August 2021
Revised: 12 April 2022
Accepted: 11 June 2022
Published: 11 September 2022
Authors
Radhika Ganapathy
Department of Mathematics
Indian Institute of Science
Bengaluru
India