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Products and symmetrized powers of irreducible representations of SO*(2n)

Record type: Article

The calculation of branching rules, tensor products and plethysms of the infinite-dimensional harmonic series unitary irreducible representations of the non-compact group is considered and the duality between and Sp(2k) exploited. The branching rule for the restriction of an arbitrary harmonic series irreducible representation of to U(n) is derived, and the decomposition is given explicitly for each of the infinite number of fundamental harmonic series irreducible representations, , of whose direct sum constitutes the metaplectic representation, H, of . A concise expression for the decomposition of tensor products is derived and a complete analysis of the terms in both and is given. A general formula for plethysms of arbitrary irreducible representations of is derived and its implementation illustrated both by means of a detailed generic example and by a complete determination of the symmetric and antisymmetric terms of . Finally, relationships that arise from the embedding of the product groups and in the metaplectic group Mp(4nk) are discussed.

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Citation

King, R.C., Toumazet, F. and Wybourne, B.G. (1998) Products and symmetrized powers of irreducible representations of SO*(2n) Journal of Physics A: Mathematical and General, 31, (31), pp. 6691-6705. (doi:10.1088/0305-4470/31/31/014).

More information

Published date: 1998
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29518
URI: http://eprints.soton.ac.uk/id/eprint/29518
ISSN: 0305-4470
PURE UUID: c75be829-eb0f-4eb6-b891-71564bbf8d5f

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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: F. Toumazet
Author: B.G. Wybourne

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