Unicity of types and local Jacquet--Langlands correspondence

Autor:	Yamamoto, Yuki
Rok vydání:	2022
Předmět:	Mathematics - Representation Theory Mathematics - Number Theory 22E50
Druh dokumentu:	Working Paper
Popis:	Let $F$ be a non-archimedean local field. For any irreducible representation $\pi$ of an inner form $G'=\mathrm{GL}_{m}(D)$ of $G=\mathrm{GL}_{N}(F)$, there exists an irredubile representation of a maximal compact open subgroup in $G'$ which is also a type for $\pi$. Then we can consider the problem whether these types are unique or not in some sense. If such types for $\pi$ are unique, we say $\pi$ has the strong unicity property of types. On the other hand, there exists a correspondence connecting irreducible representations of $G'$ and $G$, called the Jacquet--Langland correspondence. In this paper, we study the ralation between the strong unicity of types and the Jacquet--Langlands correspondence. Comment: 5 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.05252 Zobrazit plný text záznamu View this record from Arxiv