ABSTRACT CARRIER SPACE FORMALISM FOR THE IRREDUCIBLE TENSOR-OPERATORSOF COMPACT QUANTUM GROUP-ALGEBRAS

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.