Comparison of types for inner forms of $\mathrm{GL}_{N}$

Yuki Yamamoto

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arXiv · 2005.02622

Comparison of types for 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 $A$. To construct types for supercuspidal representations of $G$, simple types by S\'echerre--Stevens and Yu's construction are already known. In this paper, we compare these constructions. In particular, we show essentially tame supercuspidal representations of $G$ defined by Bushnell--Henniart are nothing but tame supercuspidal representations defined by Yu.

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Yuki Yamamoto. 2020-05-06. Comparison of types for inner forms of $\mathrm{GL}_{N}$. https://arxiv.org/abs/2005.02622

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