Howe correspondence for reductive groups over finite fields
type: Item
instance of: scholarly article
title: Howe correspondence for reductive groups over finite fields
zbMATH Open document ID: 0856.22027
DOI: 10.1215/S0012-7094-96-08312-X
author: Jean Michel
author: Raphaël Rouquier
author: Anne-Marie Aubert
published in: Duke Mathematical Journal
publication date: 1997-02-03T00:00:00Z
review text: Let \(\mathbb{F}_q\) be a finite field with odd characteristic \(p\). Let \((G, G')\) be a pair of subgroups of \(\text{Sp}_{2n}(\mathbb{F}_q)\) which are centralizers of each other and are a dual reductive (irreducible) pair. Assume \[ (G, G')= \begin{cases} (\text{Sp}_{2m}(\mathbb{F}_q),\quad O^{\pm}_{2m'}(\mathbb{F}_q))\qquad n= 2mm'\\ (\text{Sp}_{2m}(q),\quad O_{2m'+ 1}(q)\qquad n= m(2m'+ 1)\\ \text{or } (U_m(q),\;U_{m'}(q))\text{ or } (\text{GL}_m(q),\;\text{GL}_{m'}(q))\quad n= mm'.\end{cases} \] The purpose of the article under review is to describe the Howe correspondence arising from restricting the Weil representation \(\omega\) of \(\text{Sp}_{2n}(q)\) to \(G\times G'\).
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 912129
zbMATH Keywords: finite field
zbMATH Keywords: dual reductive (irreducible) pair
zbMATH Keywords: Howe correspondence
zbMATH Keywords: Weil representation
describes a project that uses: GAP
MaRDI profile type: Publication
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full work available at URL: s0012-7094-96-08312-x
OpenAlex ID: W1572174884
description: scientific article; zbMATH DE number 912129