Jf. Cornwell, IRREDUCIBLE TENSOR-OPERATORS IN THE REGULAR COACTION FORMALISMS OF COMPACT QUANTUM GROUP-ALGEBRAS, Journal of mathematical physics, 37(9), 1996, pp. 4590-4634
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.