A generalized Weil representation for \(\text{SL}_*(2,A_m)\), where \(A_m=\mathbb{F}_q[x]\langle x^m\rangle\).
type: Item
instance of: scholarly article
title: A generalized Weil representation for \(\text{SL}_*(2,A_m)\), where \(A_m=\mathbb{F}_q[x]\langle x^m\rangle\).
zbMATH Open document ID: 1179.20045
author: Luis Gutiérrez Frez
published in: Journal of Algebra
publication date: 2009-09-10T00:00:00Z
review text: Let \(k\) be a finite field of odd order, \(m\) a positive integer, \(A_m=k[x]/(x^m)\). The involution \(^*\) on \(A_m\) is defined by \(x^*=-x\). The other involutions are classified. A presentation of the unitary group \(\text{SL}_*(2,A_m)\) of the standard skew-Hermitian matrix \(\left(\begin{smallmatrix} 0&1\\ -1& 0\end{smallmatrix}\right)\) is given, and a Weil representation of this group is constructed.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 5602638
zbMATH Keywords: Weil representations
zbMATH Keywords: twisted groups
zbMATH Keywords: rings with involution
zbMATH Keywords: special linear groups
zbMATH Keywords: presentations
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.03.033
OpenAlex ID: W2170238231
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DOI: 10.1016/J.JALGEBRA.2009.03.033
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description: scientific article; zbMATH DE number 5602638