On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$

Yuki Yamamoto

On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$

Number Theory 2019-11-13 v2 Representation 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 $A$ . It is known that for every irreducible supercuspidal representation $\pi$ , there exists a $[G, \pi]_{G}$ -type $(J, \lambda)$ , called a (maximal) simple type. We will show that $[G, \pi]_{G}$ -types defined over some maximal compact subgroup are unique up to $G$ -conjugations under some unramifiedness assumption on a simple stratum.

Keywords

supercuspidal representations inner forms of gl_n simple types non-archimedean local field central simple algebra maximal compact subgroup g-conjugation

Cite

@article{arxiv.1909.10748,
  title  = {On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$},
  author = {Yuki Yamamoto},
  journal= {arXiv preprint arXiv:1909.10748},
  year   = {2019}
}

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28 pages

On the types for supercuspidal representations of inner forms of $\mathrm{GL}_{N}$

Abstract

Keywords

Cite

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