Year: 2026
Type: preprint
Abstract: Let $F$ be a nonarchimedean local field of characteristic zero and residue characteristic $p$. Let $E$ be a quadratic field extension of $F$. Let $D$ be the unique quaternion division algebra defined over $F$. Let $G=\GL_{2}(E)$ and $H=D^\times$. This paper studies the modulo distinction problem for the pair $(G,H)$ with $\ell\neq p$, which gives a complete classification of $H$-distinguished representations of $G$, including the cases $\ell=2$ and $p=2$. In terms of type theory, we give a complete classification of $H$-distinguished supercuspidal representations when $p$ is odd.
Source: arXiv (Cornell University)
Authors: Liu, Junyan, Lu, Hengfei
Institution: Beihang University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221778399