Abstract
The multiplicity problem of r-fold tensor products of irreducible representations of Sp(2k, C) are considered. The arbitrary r-fold tensor product is shown to be isomorphic to a subspace of the holomorphic Hilbert (Bargmann) space of n*2k complex variables. Maps are constructed which carry an irreducible representation of Sp(2k, C) into this subspace. An algebra of commuting operators is constructed and it is shown how eigenvalues and eigenvectors of certain of these operators can be used to resolve the multiplicity.
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