On resolving the multiplicity of arbitrary tensor products of the U(N) groups
- 21 October 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (20), 3877-3892
- https://doi.org/10.1088/0305-4470/21/20/008
Abstract
Representations of U(N) are realised as right translations on holomorphic Hilbert (Bargmann) spaces of n*N complex variables. r-fold tensor product spaces of irreducible representations of U(N) are shown to be isomorphic to subspaces of the holomorphic Hilbert spaces. Maps are exhibited which carry an irreducible representation of U(N) into these subspaces. The algebra of operators commuting with these maps is constructed and it is shown how eigenvalues of certain of these operators can be used to resolve the multiplicity. Several examples from U(3) are explicitly worked out.Keywords
This publication has 11 references indexed in Scilit:
- New perspective on the U(n) Wigner-Racah calculus. II. Elementary reduced Wigner coefficients for U(n)Journal of Physics A: General Physics, 1987
- A resolution of the SU(3) outer multiplicity problem and computation of Wigner coefficients for SU(3)Journal of Physics A: General Physics, 1986
- Canonical orthonormal basis for SU(3)⊃SO(3). II. Reduced matrix elements of the SU(3) generatorsJournal of Physics A: General Physics, 1985
- On the structure of tensor operators in SU3Communications in Mathematical Physics, 1984
- The invariant theory of n × n matricesAdvances in Mathematics, 1976
- Noninvariance Groups in the Second-Quantization Picture and Their ApplicationsJournal of Mathematical Physics, 1970
- Recent Progress Toward a Theory of Tensor Operators in the Unitary GroupsAmerican Journal of Physics, 1970
- Recursion Relations for the Wigner Coefficients of Unitary GroupsJournal of Mathematical Physics, 1965
- Bases for the Irreducible Representations of the Unitary Groups and Some ApplicationsJournal of Mathematical Physics, 1963
- A formula for the multiplicity of a weightTransactions of the American Mathematical Society, 1959