Year: 2018
Type: preprint
Abstract: Let ${\bf G}$ be a split classical group over a non-Archimedean local field $F$ with the cardinality of the residue field $q_F>5$. Let $M$ be the group of $F$-points of a Levi factor of a proper $F$-parabolic subgroup of ${\bf G}$. Let $[M, σ_M]_M$ be an inertial class such that $σ_M$ contains a depth-zero Moy--Prasad type of the form $(K_M, τ_M)$, where $K_M$ is a hyperspecial maximal compact subgroup of $M$. Let $K$ be a hyperspecial maximal compact subgroup of ${\bf G}(F)$ such that $K$ contains $K_M$. In this article, we classify $\mathfrak{s}$-typical representations of $K$. In particular, we show that the $\mathfrak{s}$-typical representations of $K$ are precisely the irreducible subrepresentations of $\ind_J^Kλ$, where $(J, λ)$ is a level-zero $G$-cover of $(K\cap M, τ_M)$.
Source: arXiv (Cornell University)
Authors: Mondal, Amiya Kumar, Nadimpalli, Santosh
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2894643575