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

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

Representation Theory 2024-07-02 v2 Number Theory

Authors: Arnaud Mayeux , Yuki Yamamoto

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.

Keywords

supercuspidal representations types gl_n inner forms bushnell-kutzko secherre yu's construction

Cite

@article{arxiv.2112.12367,
  title  = {Comparing Bushnell-Kutzko and S\'echerre's constructions of types for $\mathrm{GL}_{N}$ and its inner forms with Yu's construction},
  author = {Arnaud Mayeux and Yuki Yamamoto},
  journal= {arXiv preprint arXiv:2112.12367},
  year   = {2024}
}

Comments

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

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

Abstract

Keywords

Cite

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