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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.00785 |
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Table of Contents:
- Let $G$ be a connected split reductive group defined over $\mathbb{Z}$. Let $F$ and $F'$ be two non-Archimedean $m$-close local fields, where $m$ is a positive integer. D.Kazhdan gave an isomorphism between the Hecke algebras ${\rm Kaz}_m^F :\mathcal{H}\big(G(F),K_F\big) \rightarrow \mathcal{H}\big(G(F'),K_{F'}\big)$, where $K_F$ and $K_{F'}$ are the $m$-th usual congruence subgroups of $G(F)$ and $G(F')$ respectively. On the other hand, if $σ$ is an automorphism of $G$ of prime order $l$, then we have Brauer homomorphism ${\rm Br}:\mathcal{H}(G(F),U(F))\rightarrow \mathcal{H}(G^σ(F),U^σ(F))$, where $U(F)$ and $U^σ(F)$ are compact open subgroups of $G(F)$ and $G^σ(F)$ respectively. In this article, we study the compatibility between these two maps in the local base change setting. Further, an application of this compatibility is given in the context of linkage--which is the representation theoretic version of Brauer homomorphism.