Comparing Bushnell-Kutzko and Sécherre's constructions of types for ${\mathrm{GL}}_N$ and its inner forms with Yu's construction

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 Sécherre 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.

61 pages. To appear in Bull. Soc. Math. France

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