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Bibliographic Details
Main Author: Matringe, Nadir
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.08393
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author Matringe, Nadir
author_facet Matringe, Nadir
contents Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $θ$. Under the assumption that there exists a maximally $θ$-split torus in $\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations of Kato and Takano.
format Preprint
id arxiv_https___arxiv_org_abs_2506_08393
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On relative cuspidality
Matringe, Nadir
Representation Theory
Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $θ$. Under the assumption that there exists a maximally $θ$-split torus in $\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations of Kato and Takano.
title On relative cuspidality
topic Representation Theory
url https://arxiv.org/abs/2506.08393