Comparing Bushnell-Kutzko and S\'echerre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction

Arnaud Mayeux; Yuki Yamamoto

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arXiv · 2112.12367

Comparing Bushnell-Kutzko and S\'echerre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction

Arnaud Mayeux·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 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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Arnaud Mayeux, Yuki Yamamoto. 2021-12-23. Comparing Bushnell-Kutzko and S\'echerre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction. https://arxiv.org/abs/2112.12367

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