Uniqueness of generalized Waldspurger model for \(GL(2n)\)
type: Item
instance of: scholarly article
title: Uniqueness of generalized Waldspurger model for \(GL(2n)\)
zbMATH Open document ID: 0897.11016
author: Jiandong Guo
published in: Pacific Journal of Mathematics
publication date: 1998-05-24T00:00:00Z
review text: Let \(F\) be a non-archimedean local field of characteristic zero. Let \(D\) be either the quaternion field over \(F\) or the algebra of two by two matrices over \(F\). Denote by \(G\) the group \(GL(n,D)\) and by \(H\) its subgroup \(GL(n,E)\), where \(E\) is a quadratic extension of \(F\) imbedded in \(D\). It is proved in the paper that for any \(g\in G\) one has \(g^{-1} \in HgH\). As a consequence, there can be at most one \(H\)-invariant linear form (up to a scalar factor) on the space of an irreducible admissible representation of \(G\). For the case where \(D\) is the algebra of two by two matrices and \(E=F\times F\) [see \textit{H. Jacquet} and \textit{S. Rallis}, Uniqueness of linear periods, Compos. Math. 102, 65-123 (1996; Zbl 0855.22018)].
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 1136629
zbMATH Keywords: generalized Waldspurger model
zbMATH Keywords: quaternion field
zbMATH Keywords: algebra of two by two matrices
zbMATH Keywords: \(H\)-invariant linear forms
zbMATH Keywords: space of an irreducible admissible representation
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
full work available at URL: pjm.1997.180.273
OpenAlex ID: W2005514350
DOI: 10.2140/PJM.1997.180.273
description: scientific article; zbMATH DE number 1136629