IRREDUCIBLE TENSOR-OPERATORS IN THE REGULAR COACTION FORMALISMS OF COMPACT QUANTUM GROUP-ALGEBRAS

The defining conditions for the irreducible tensor operators associate d with the unitary irreducible corepresentations of compact quantum gr oup algebras are deduced first in both the right and left regular coac tion formalisms. In each case it is shown that there are two types of irreducible tensor operator, which may be called ''ordinary'' and ''tw isted.'' The consistency of the definitions is demonstrated, and vario us consequences are deduced, including generalizations of the Wigner-E ckart theorem for both the ordinary and twisted operators. Also includ ed are discussions (within the regular coaction formalisms for compact quantum group algebras) of inner-products, basis functions, projectio n operators, Clebsch-Gordan coefficients, and two types of tensor prod uct of corepresentations. The formulation of quantum homogeneous space s for compact quantum group algebras is discussed, and the defining co nditions for the irreducible tensor operators associated with such qua ntum homogeneous spaces and with the unitary irreducible corepresentat ions 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 ordin ary and twisted irreducible tensor operators. Various consequences are deduced, including the corresponding generalizations of the Wigner-Ec kart theorem. (C) 1996 American Institute of Physics.