The University of Southampton
University of Southampton Institutional Repository

The place of the adjoint representation in the Kronecker square of irreducible representations of simple Lie groups

The place of the adjoint representation in the Kronecker square of irreducible representations of simple Lie groups
The place of the adjoint representation in the Kronecker square of irreducible representations of simple Lie groups
The multiplicity of occurrence of the adjoint representation in the decomposition of the square of any finite-dimensional irreducible representation of any compact simple Lie group is shown to be equal to the number of non-vanishing components of the Dynkin label of . The resolution of this multiplicity into contributions to the symmetric and antisymmetric squares of is discussed, with complete results being found for all of the classical and some of the exceptional simple Lie groups, and partial results culminating in conjectures for the remaining exceptional groups.
0305-4470
5059-5077
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Wybourne, B.G.
527c5e72-79db-40a6-901c-284a3bd788dc
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Wybourne, B.G.
527c5e72-79db-40a6-901c-284a3bd788dc

King, R.C. and Wybourne, B.G. (1996) The place of the adjoint representation in the Kronecker square of irreducible representations of simple Lie groups. Journal of Physics A: Mathematical and General, 29 (16), 5059-5077. (doi:10.1088/0305-4470/29/16/026).

Record type: Article

Abstract

The multiplicity of occurrence of the adjoint representation in the decomposition of the square of any finite-dimensional irreducible representation of any compact simple Lie group is shown to be equal to the number of non-vanishing components of the Dynkin label of . The resolution of this multiplicity into contributions to the symmetric and antisymmetric squares of is discussed, with complete results being found for all of the classical and some of the exceptional simple Lie groups, and partial results culminating in conjectures for the remaining exceptional groups.

This record has no associated files available for download.

More information

Published date: 1996
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29514
URI: http://eprints.soton.ac.uk/id/eprint/29514
ISSN: 0305-4470
PURE UUID: ec3f55ab-6777-43b5-b323-805126ebb79d

Catalogue record

Date deposited: 21 Dec 2006
Last modified: 15 Mar 2024 07:32

Export record

Altmetrics

Contributors

Author: R.C. King
Author: B.G. Wybourne

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×