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(1972)
Multiplicity can be computed using Steinberg's formula, see
W. Klink, T. Ton-That, R. Wills (1993)
Shift operators and the U(N) multiplicity problemJournal of Physics A, 26
Roger Godement (1982)
Introduction a la Th?eorie des Groupes de Lie
The U( N ) irreducible representation spaces are all realized as polynomials over matrix complex variables satisfying certain conditions
ii) A subspace W of V is R -invariant if and only if it is ˜ R -invariant
W. Klink, T. Ton-That (1992)
Invariant theory of the block diagonal subgroups of GL(n,C) and generalized Casimir operatorsJournal of Algebra, 145
W. Klink, T. Ton-That (1989)
Calculation of Clebsch-Gordan and Racah coefficients using symbolic manipulatio n programsJournal of Computational Physics, 80
R Aulwes, W. Klink, T. Ton-That (2001)
Invariant theory, generalized Casimir operators, and tensor product decompositions of U(N)Journal of Physics A: Mathematical and General, 34
W. Klink, T. Ton-That (1988)
On resolving the multiplicity of arbitrary tensor products of the U(N) groupsJournal of Physics A, 21
W. Thompson, L. Cook (1994)
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W. Klink, T. Ton-That (1989)
n-Fold tensor products of GL(N,C) and decomposition of fock spacesJournal of Functional Analysis, 84
(1986)
theory is discussed
D. Mattis (1981)
Quantum Theory of Angular Momentum
Algorithms are developed for computing generalized Racah coefficients for the U(N) groups. The irreducible representations (irreps) of the U(N) groups, as well as their tensor products, are realized as polynomials in complex variables. When tensor product irrep labels as well as a given irrep label are specified, maps are constructed from the irrep space to the tensor product space. The number of linearly independent maps gives the multiplicity. The main theorem of this paper shows that the eigenvalues of generalized Casimir operators are always sufficient to break the multiplicity. Using this theorem algorithms are given for computing the overlap between different sets of eigenvalues of commuting generalized Casimir operators, which are the generalized Racah coefficients. It is also shown that these coefficients are basis independent.
Acta Applicandae Mathematicae – Springer Journals
Published: Jun 4, 2005
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