The dual pair \((U(1),U(1))\) over a \(p\)-adic field
type: Item
instance of: scholarly article
title: The dual pair \((U(1),U(1))\) over a \(p\)-adic field
zbMATH Open document ID: 0789.22034
author: Courtney Moen
published in: Pacific Journal of Mathematics
publication date: 1994-03-01T00:00:00Z
review text: Let \(F\) denote a \(p\)-adic field with \(p \neq 2\) and \(n\) a natural number. The metaplectic group \(MSL_ n(F)\) is the nontrivial two-sheeted covering group of \(SL_ n(F)\). The metaplectic representation was introduced by A. Weil and it rules the theory of theta series and theta correspondences. A theta correspondence is thus given by the restriction of the metaplectic representation to a dual reductive pair \((G,G')\) in \(MSL_ n (F)\) which defines a correspondence between representations of \(G\) and representations of \(G'\). In the paper under consideration one of the simplest cases: \(n=2\), \(G=G'=U(1)\) is treated and the restriction of the metaplectic representation to \(G\) is explicitly computed.
reviewed by: Anton Deitmar
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 509109
zbMATH Keywords: Weil representation
zbMATH Keywords: \(p\)-adic field
zbMATH Keywords: metaplectic group
zbMATH Keywords: theta correspondences
zbMATH Keywords: dual reductive pair
zbMATH Keywords: metaplectic representation
MaRDI profile type: Publication
full work available at URL: pjm.1993.158.365
OpenAlex ID: W2005576493
DOI: 10.2140/PJM.1993.158.365
description: scientific article; zbMATH DE number 509109