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

Yuki Yamamoto

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

Representation Theory 2020-06-16 v2 Number Theory

Authors: 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--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.

Keywords

inner forms general linear group supercuspidal representations simple types yu's construction essentially tame

Cite

@article{arxiv.2005.02622,
  title  = {Comparison of types for inner forms of $\mathrm{GL}_{N}$},
  author = {Yuki Yamamoto},
  journal= {arXiv preprint arXiv:2005.02622},
  year   = {2020}
}

Comments

47 pages

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