ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The explicit denominator (normalization) function of the canonical tensor operators of the quantum algebra uq(3), corresponding to the maximal null space case is derived ab initio in terms of double basic hypergeometric series, which cannot be obtained as any q-extension of the SU(3) denominator polynomial Gb″1(Δ,x) in terms of multiple (double or triple) balanced hypergeometric series, introduced by Biedenharn, Louck, and their collaborators (although their q=1 versions are shown being equivalent). The corresponding orthonormal seed isoscalar factors of the coupling (Wigner–Clebsch–Gordan) coefficients of uq(3) and SU(3) with multiple irreducible representations are presented. Conjectured expression of the q-polynomials [which ratios appear in the uq(3) and (new) SU(3) denominator functions for an arbitrary value of the canonical multiplicity label t of the repeating irreducible representations] in terms of multiple partition dependent q-series (extension of the maximal and minimal null space versions) is presented and considered. © 1999 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.533063
