A Cauchy Harish-Chandra integral, for a real reductive dual pair
type: Item
instance of: scholarly article
title: A Cauchy Harish-Chandra integral, for a real reductive dual pair
zbMATH Open document ID: 0953.22014
author: Tomasz Przebinda
published in: Inventiones Mathematicae
publication date: 2001-01-22T00:00:00Z
review text: For a real irreducible dual pair \(G\), \(G'\) in a metaplectic group, with \(\text{rank }G\leq \text{rank }G'\), the author constructs an integral kernel operator from the space of invariant eigendistributions on \(G\) to the space of invariant distributions on \(G'\), and conjectures that this operator is compatible with Howe's correspondence on the level of characters. The construction indicates a direct link between the Cauchy determinant identity and the Howe correspondence.
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 1502076
zbMATH Keywords: Cauchy identity
zbMATH Keywords: action
zbMATH Keywords: character
zbMATH Keywords: trace
zbMATH Keywords: classical invariant theory
zbMATH Keywords: real irreducible dual pair
zbMATH Keywords: metaplectic group
zbMATH Keywords: Cauchy determinant identity
zbMATH Keywords: Cauchy Harish Chandra integral
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: s002220000070
OpenAlex ID: W2019319622
DOI: 10.1007/S002220000070
description: scientific article; zbMATH DE number 1502076