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.
5059-5077
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Wybourne, B.G.
527c5e72-79db-40a6-901c-284a3bd788dc
1996
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), .
(doi:10.1088/0305-4470/29/16/026).
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