Jf. Cornwell, ABSTRACT CARRIER SPACE FORMALISM FOR THE IRREDUCIBLE TENSOR-OPERATORSOF COMPACT QUANTUM GROUP-ALGEBRAS, Journal of mathematical physics, 37(6), 1996, pp. 2934-2954
Defining conditions for irreducible tensor operators associated with t
he unitary irreducible corepresentations of compact quantum group alge
bras are deduced within the framework of the abstract carrier space fo
rmalism. It is shown that there are two types of irreducible tensor op
erator, which may be called 'ordinary' and 'twisted'. The consistency
of the definitions is demonstrated, and various consequences are deduc
ed, including generalizations of the Wigner-Eckart theorem for both th
e ordinary and twisted operators. Examples of irreducible tensor opera
tors for the standard deformation of the function algebra of the compa
ct Lie group SU(2) are described to demonstrate the applicability of t
he new definitions. (C) 1996 American Institute of Physics.