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首页> 外文期刊>Journal of Mathematical Physics >IRREDUCIBLE TENSOR OPERATORS IN THE REGULAR COACTION FORMALISMS OF COMPACT QUANTUM GROUP ALGEBRAS
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IRREDUCIBLE TENSOR OPERATORS IN THE REGULAR COACTION FORMALISMS OF COMPACT QUANTUM GROUP ALGEBRAS

机译：紧量子群代数的正规作用形式中的不可约张量算子

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The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentations 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 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 quantum homogeneous spaces and with the unitary irreducible corepresentations 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. (C) 1996 American Institute of Physics. [References: 37]
机译：与紧凑型量子群代数的单位不可约核表示相关的不可约张量算符的定义条件首先在左右正则合作形式主义中推导。在每种情况下，都表明存在两种类型的不可约张量算符，分别称为“普通”和“扭曲”。证明了定义的一致性，并得出了各种结果，包括对普通算子和扭曲算子的Wigner-Eckart定理。还包括内部乘积，基函数，投影算子，Clebsch-Gordan系数和核心表示的两种张量积的讨论（在紧凑型量子群代数的常规合作式形式内）。讨论了紧凑型量子群代数的量子同质空间的表示，并推导了与此类量子同质空间以及紧凑型量子群代数的单位不可约核表示相关的不可约张量算符的定义条件。有两个版本，分别对应左右常规协作的限制。在每种情况下，再次表明存在普通且扭曲的不可约张量算子。推断出各种结果，包括Wigner-Eckart定理的相应概括。 （C）1996年美国物理研究所。 [参考：37]

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