Abstract
An explicit realization of the normalized Gel’fand–(Weyl)–Zetlin (GWZ) basis for Uq(sl(3)) in terms of polynomial functions in three variables (real or complex) is given. The construction uses two different realizations of the Uq(sl(3)) unnormalized GWZ basis which were given previously, and whose transformation properties were not known. It turns out that finding these properties enables us to find the (GWZ-dependent) proportionality constant between these two realizations. The scalar product is also fixed by this in both unnormalized realizations, and then, by normalization, the normalized GWZ states are obtained. As by-products new summation formulas are obtained which seem new also for q=1. The main new formula is a double sum which is given in terms of the proportionality constant mentioned above. This double sum can be written as single sum over a q−3F2 hypergeometric function, or as a q-hypergeometric function of two variables.
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