Wigner-Eckart theorem for tensor operators of Hopf algebras

Details Wigner-Eckart theorem for tensor operators of Hopf algebras Wigner-Eckart theorem for tensor operators of Hopf algebras

2004-04-06

arxiv.org/abs/math-ph/0404019v1

Physics

Mathematical Physics

14 pages, latex

Scientific paper

We prove Wigner-Eckart theorem for the irreducible tensor operators for arbitrary Hopf algebras, provided that tensor product of their irreducible representation is completely reducible. The proof is based on the properties of the irreducible representations of Hopf algebras, in particular on Schur lemma. Two classes of tensor operators for the Hopf algebra U$_{t}$(su(2)) are considered. The reduced matrix elements for the class of irreducible tensor operators are calculated. A construction of some elements of the center of U$_{t}$(su(2)) is given.

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