Contiguity relations for \(q\)-hypergeometric function and related quantum group (Q1803562)

The author has expressed the contiguity relations for \(q\)-hypergeometric series in terms of the shift operator \(Tf(x)=f(qx)\) and \(q\)-difference operators \[ [\theta+\alpha]_ q={q^ \alpha T-q^{-\alpha}T^{- 1}\over q-q^{-1}},\quad\text{where } [A]_ q={q^ A-q^{-A}\over q- q^{-1}} \] for any number \(A\). He has also established that certain contiguity operators acting on Heine's series give a representation of the \(q\)-analogue \(U_ q(SL(4))\) of the universal enveloping algebra of the Lie group \(SL(4)\).