Decompositions of tensor products of infinite and finite dimensional representations of semisimple groups
type: Item
instance of: scholarly article
title: Decompositions of tensor products of infinite and finite dimensional representations of semisimple groups
zbMATH Open document ID: 0574.22009
author: Kyo Nishiyama
published in: Journal of Mathematics of Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: Let G be a connected semisimple Lie group with finite centre, A a Harish- Chandra G-module, F a finite-dimensional simple G-module. In the first part decomposition formulas are derived for the Harish-Chandra character of \(F\otimes A\) on a Cartan subgroup if A belongs to the principal series or to the discrete series. In the second part these formulas are used for the case that G is a Lorentz group and A is simple to obtain the decomposition of the character of \(F\otimes A\) into irreducible characters, by means of T. Hirai's description of the irreducible characters of the Lorentz groups.
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 3916602
zbMATH Keywords: Harish-Chandra module
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: Lorentz group
zbMATH Keywords: irreducible characters
reviewed by: H. de Vries
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521155
OpenAlex ID: W1529412632
DOI: 10.1215/KJM/1250521155
description: scientific article; zbMATH DE number 3916602