Products and symmetrized powers of irreducible representations of SO*(2n)
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), 66916705. (doi:10.1088/03054470/31/31/014).
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Description/Abstract
The calculation of branching rules, tensor products and plethysms of the infinitedimensional harmonic series unitary irreducible representations of the noncompact 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.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1088/03054470/31/31/014  
Related URLs:  
Subjects:  Q Science > QA Mathematics  
Divisions :  University Structure  Pre August 2011 > School of Mathematics > Applied Mathematics 

ePrint ID:  29518  
Accepted Date and Publication Date: 


Date Deposited:  21 Dec 2006  
Last Modified:  31 Mar 2016 11:55  
URI:  http://eprints.soton.ac.uk/id/eprint/29518 
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