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arXiv · 2606.05192

A problem on Hecke algebras for $\mathrm{GL}_n(F)$ for $n>2$ over $p$-adic field $F$

Subha Sandeep Repaka
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Abstract

We study the Hecke algebra $\mathcal{H}_G(F)$ for $G = \mathrm{GL}_n$ and $n>2$ where $F$ is a non-Archimedean local field of characteristic zero. We show that for $G = \mathrm{GL}_n$ and $n>2$ and any two such fields $E$ and $F$, there is a Morita equivalence $\mathcal{H}_G(E) \sim \mathcal{H}_G(F)$, by using the Bernstein decomposition of the Hecke algebra and by determining the intertwining algebras that yield the Bernstein blocks up to Morita equivalence.

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BibTeXRIS

Subha Sandeep Repaka. 2026-05-07. A problem on Hecke algebras for $\mathrm{GL}_n(F)$ for $n>2$ over $p$-adic field $F$. https://arxiv.org/abs/2606.05192

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