Branching of representations to symmetric subgroups
type: Item
instance of: scholarly article
zbMATH Open document ID: 1239.22011
author: Joseph A. Wolf
author: M. Eastwood
publication date: 2012-05-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/0812.0822
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 6032505
zbMATH Keywords: branching
zbMATH Keywords: representation
zbMATH Keywords: compact Lie group
zbMATH Keywords: Lie algebra
MaRDI profile type: Publication
arXiv ID: 0812.0822
arXiv classification: math.RT
arXiv classification: math.AG
title: Branching of representations to symmetric subgroups
published in: Münster Journal of Mathematics
review text: Given a Lie algebra \(\mathfrak g\) and its subalgebra \(\mathfrak k\), the branching problem studies the restriction of a representation of \(\mathfrak g\) to \(\mathfrak k\). This article focuses on the branching problem where \(\mathfrak g\) is the Lie algebra of a compact Lie group, and \(\mathfrak k\) is the fixed point set \({\mathfrak g}^\theta\) of an automorphism \(\theta\) on \(\mathfrak g\). It presents a computing program for this purpose, known as the LiE program, available at \url{http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/}.NEWLINENEWLINEIt uses the LiE program to work out several cases where \(\theta\) has order 2, 3 and 5, and also where \(\mathfrak k\) is the centralizer of a toral subalgebra of \(\mathfrak g\).
reviewed by: Meng-Kiat Chuah
description: scientific article; zbMATH DE number 6032505