Representations of Sn*U(N) in repeated tensor products of the unitary groups
- 7 July 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (13), 2751-2763
- https://doi.org/10.1088/0305-4470/23/13/014
Abstract
The n-fold tensor product space generated by a given irreducible representation of the unitary group U(N) is a representation space for the symmetric group Sn as well as for U(N). Using ideas from the theory of dual pairs, such tensor product spaces are decomposed into irreducible representations of U(N) times reducible representations of Sn. Computationally effective formulae for the multiplicity of irreducible representations of Sn are given. Generating sets of invariant polynomials from the enveloping algebra of U(N) that commute with the Sn action are exhibited; it is shown that the eigenvalues of such operators can be used to break the multiplicity occurring in the dual U(N)xSn action.Keywords
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