On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$

Yuki Yamamoto

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arXiv · 1909.10748

On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$

Yuki Yamamoto

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Abstract

Let $F$ be a non-Archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. It is known that for every irreducible supercuspidal representation $π$, there exists a $[G, π]_{G}$-type $(J, λ)$, called a (maximal) simple type. We will show that $[G, π]_{G}$-types defined over some maximal compact subgroup are unique up to $G$-conjugations under some unramifiedness assumption on a simple stratum.

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Yuki Yamamoto. 2019-11-12. On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$. https://arxiv.org/abs/1909.10748

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