A Hecke algebra isomorphism over close local fields

Let $G$ be a split connected reductive group over $ℤ$ . Let $F$ be a nonarchimedean local field. With $K_{m} : = Ker (G (𝔒_{F}) \to G (𝔒_{F} ∕ 𝔭_{F}^{m}))$ , Kazhdan proved that for a field $F^{'}$ sufficiently close local field to $F$ , the Hecke algebras $ℋ (G (F), K_{m})$ and $ℋ (G (F^{'}), K_{m}^{'})$ are isomorphic, where $K_{m}^{'}$ 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

Vol. 319, No. 2, 2022

Radhika Ganapathy

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors