Irreducible Tensor Operators
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Wigner-eckart Theorem for Tensor Operators of Hopf Algebras
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 Ut(su(2)) are considered. The reduced...
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carrier space formalism for the irreducible tensor operators of compact quantum group algebras Abstract Defining conditions for irreducible tensor operators associated with the uni-tary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that there are two types of irreducible tensor operator, whic...
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Tensor operators in graded representations of Z2−graded Hopf algebras are defined and their elementary properties are derived. WignerEckart theorem for irreducible tensor operators for Uq[osp(1 | 2)] is proven. Examples of tensor operators in the irreducible representation space of Hopf algebra Uq[osp(1 | 2)] are considered. The reduced matrix elements for the irreducible tensor operators are c...
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The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it is shown that there are two types of irreducible tensor operator , which may be called 'ordinary' and 'twisted'. The consistency of the definitions is demon...
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