Towards the canonical tensor operators of u q(3). I. The maximal null space case

Abstract

Generalizing the SU(3) canonical tensor operator concept (Biedenharn and Louck) to the quantum algebra uq(3), the Wigner–Clebsch–Gordan coefficients of uq(3) with repeating irreducible representations are considered. Extremal projectors of the quantum algebra uq(3) in terms of the ordered generator polynomials are used for evaluation of the bilinear combinations of the uq(3) canonical isoscalar factors. Explicit expressions of the uq(3) isofactors, corresponding to the maximal null space case of the uq(3) unit canonical tensor operators, and their normalization factors (denominator functions) are presented. The transposition and conjugation phase factors for the SU(3) and uq(3) canonical isofactors are correlated with phases and zeros of boundary isofactors. Invariance of the canonical isofactors (or absence of such invariance) under interchange of the tensor operator and the initial or final state parameters is correlated with the existence and invariance (or numerical degeneracy) of the usual splitting (distinctive) conditions. Some oversights of previous publications are disclosed.