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arXiv · 2101.01873

Hecke algebras for tame supercuspidal types

Kazuma Ohara
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Abstract

Let $F$ be a non-archimedean local field of residue characteristic $p\neq 2$. Let $G$ be a connected reductive group over $F$ that splits over a tamely ramified extension of $F$. Yu constructed types which are called tame supercuspidal types and conjectured that Hecke algebras associated with these types are isomorphic to Hecke algebras associated with depth-zero types of some twisted Levi subgroups of $G$. In this paper, we prove this conjecture. We also prove that the Hecke algebra associated with a regular supercuspidal type is isomorphic to the group algebra of a certain abelian group.

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Kazuma Ohara. 2021-01-06. Hecke algebras for tame supercuspidal types. https://arxiv.org/abs/2101.01873

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