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

Record type: Article

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.

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Citation

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), pp. 5059-5077. (doi:10.1088/0305-4470/29/16/026).

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

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Date deposited: 21 Dec 2006
Last modified: 17 Jul 2017 15:57

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Contributors

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

University divisions


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