Virtual characters and constant coefficient invariant eigendistributions on a semisimple Lie group
type: Item
instance of: scholarly article
title: Virtual characters and constant coefficient invariant eigendistributions on a semisimple Lie group
zbMATH Open document ID: 0589.22011
author: Kyo Nishiyama
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: Let G be a connected semisimple acceptable Lie group with finite center. An invariant Eigendistribution on G is a distribution which is invariant under all inner automorphisms of G and a simultaneous Eigendistribution of two-sided invariant differential operators on G. By a result of Harish-Chandra one can assign to every irreducible representation an invariant Eigendistribution, its character. The author proves that the space of invariant Eigendistributions with constant coefficients is spanned by the characters of irreducible representations.
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 3946488
zbMATH Keywords: connected semisimple acceptable Lie group
zbMATH Keywords: finite center
zbMATH Keywords: invariant Eigendistribution
zbMATH Keywords: irreducible representation
zbMATH Keywords: constant coefficients
zbMATH Keywords: characters
reviewed by: Birgit Speh
MaRDI profile type: Publication
full work available at URL: pjaa.61.168
OpenAlex ID: W2093254686
Wikidata QID: Q115219955
cites work: A property of the characters of irreducible representations of real semisimple Lie groups
cites work: The characters of some induced representations of semi-simple Lie groups
cites work: Some remarks on invariant eigendistributions on semisimple Lie groups
cites work: Q4126586
cites work: On the characters and equivalence of continuous series representations
cites work: Q3797418
cites work: Virtual character modules of semisimple Lie groups and representations of Weyl groups
DOI: 10.3792/PJAA.61.168
description: scientific article; zbMATH DE number 3946488