REPRESENTATIONS OF QUANTUM SU(3)

The problem of constructing representations of the quantum group SU(3)q ig considered. This algebra may be constructed from two sets of SU(2)q generators, oriented at an angle of 120-degrees from each other. If one makes use of known results for SU(2)q, the problem reduces to finding the transformation matrices between two sets of basis vectors, in each of which the Casimir operator for one of the SU(2)q's is diagonal. Two simple prescriptions are given for finding these matrices in a general case, using a convenient set of variables. An exact solution is given for all irreducible representations in which the maximum weight multiplicity is 2.