SO(2n+1) in an SO(2n-3)⊗SU(2)⊗SU(2) basis. I. Reduction of the symmetric representations

De Meyer, Philippe and Vanden Berghe (1982) SO(2n+1) in an SO(2n-3)⊗SU(2)⊗SU(2) basis. I. Reduction of the symmetric representations. Journal of Physics A: Mathematical and General, 15 (9). pp. 2665-2676. ISSN 0305-4470. (doi:https://doi.org/10.1088/0305-4470/15/9/017) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

Abstract

The branching rule for the reduction of symmetric irreducible unitary representations (IUR) of the simple Lie group SO(2n+1) into IUR of its maximal subgroup SO(2n-3)(X)SU(2)(X)SU(2) is established for all n>or=3. After the particular case n=3 is analysed in detail, a general proof is presented which is valid for all n>or=3. All branching rules (n=3,4,...) can be summed up in one formula. Also, a dimension verification is carried out. The generators of SO(2n+1) not belonging to the semi-simple subgroup can be combined into a mixed tensor-spinor representation with respect to the simple groups which occur in the direct product. The precise nature of that representation is indicated and discussed.

Item Type: Article
Subjects: Q Science
Divisions: Faculties > Sciences > School of Computing > Computational Intelligence Group
Depositing User: Philippe De Wilde
Date Deposited: 16 Jul 2014 08:06 UTC
Last Modified: 08 May 2018 08:43 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41763 (The current URI for this page, for reference purposes)
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