On Arthur representations and the unitary dual

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Hazeltine, Alexander, Jiang, Dihua, Liu, Baiying, Lo, Chi-Heng, Zhang, Qing
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866914316366643200
author Hazeltine, Alexander
Jiang, Dihua
Liu, Baiying
Lo, Chi-Heng
Zhang, Qing
author_facet Hazeltine, Alexander
Jiang, Dihua
Liu, Baiying
Lo, Chi-Heng
Zhang, Qing
contents In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This conjecture provides a candidate set for the unitary dual, constructed from Arthur representations. For classical groups, we develop an explicit algorithm to generate this candidate set. Evidence for its exhaustiveness includes compatibility with the known generic unitary dual, unramified unitary dual, and low-corank representations. As further support, we verify the conjecture for the unitary dual of the exceptional group of type $G_2$.
format Preprint
id arxiv_https___arxiv_org_abs_2410_11806
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On Arthur representations and the unitary dual
Hazeltine, Alexander
Jiang, Dihua
Liu, Baiying
Lo, Chi-Heng
Zhang, Qing
Representation Theory
Number Theory
In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This conjecture provides a candidate set for the unitary dual, constructed from Arthur representations. For classical groups, we develop an explicit algorithm to generate this candidate set. Evidence for its exhaustiveness includes compatibility with the known generic unitary dual, unramified unitary dual, and low-corank representations. As further support, we verify the conjecture for the unitary dual of the exceptional group of type $G_2$.
title On Arthur representations and the unitary dual
topic Representation Theory
Number Theory
url https://arxiv.org/abs/2410.11806