dorsal/arxiv
View SchemaIrreducible tensor operators in the regular coaction formalisms of compact quantum group algebras
| Authors | J. F. Cornwell |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9606001 |
| URL | https://arxiv.org/abs/q-alg/9606001 |
| DOI | 10.1063/1.531643 |
Abstract
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 {\em{two}} types of irreducible tensor operator, which may be called `ordinary' and `twisted'. The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner-Eckart theorem for both the ordinary and twisted operators. Also included are discussions (within the regular coaction formalisms for compact quantum group algebras) of inner-products, basis functions, projection operators, Clebsch-Gordan coefficients, and two types of tensor product of corepresentations. The formulation of quantum homogeneous spaces for compact quantum group algebras is discussed, and the defining conditions for the irreducible tensor operators associated with such quan! tum homogeneous spaces and with the unitary irreducible corepresentions of the compact quantum group algebras are then deduced. There are two versions, which correspond to restrictions of the right and left regular coactions. In each case it is again shown that there are ordinary and twisted irreducible tensor operators. Various consequences are deduced, including the corresponding generalizations of the Wigner-Eckart theorem.
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"abstract": "The defining conditions for the irreducible tensor operators associated with\nthe unitary irreducible corepresentions of compact quantum group algebras are\ndeduced first in both the right and left regular coaction formalisms. In each\ncase it is shown that there are {\\em{two}} types of irreducible tensor\noperator, which may be called `ordinary\u0027 and `twisted\u0027. The consistency of the\ndefinitions is demonstrated, and various consequences are deduced, including\ngeneralizations of the Wigner-Eckart theorem for both the ordinary and twisted\noperators. Also included are discussions (within the regular coaction\nformalisms for compact quantum group algebras) of inner-products, basis\nfunctions, projection operators, Clebsch-Gordan coefficients, and two types of\ntensor product of corepresentations. The formulation of quantum homogeneous\nspaces for compact quantum group algebras is discussed, and the defining\nconditions for the irreducible tensor operators associated with such quan!\n tum homogeneous spaces and with the unitary irreducible corepresentions of\nthe compact quantum group algebras are then deduced. There are two versions,\nwhich correspond to restrictions of the right and left regular coactions. In\neach case it is again shown that there are ordinary and twisted irreducible\ntensor operators. Various consequences are deduced, including the corresponding\ngeneralizations of the Wigner-Eckart theorem.",
"arxiv_id": "q-alg/9606001",
"authors": [
"J. F. Cornwell"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1063/1.531643",
"title": "Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras",
"url": "https://arxiv.org/abs/q-alg/9606001"
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