Models of irreducible \(q\)-representations of \(\operatorname{sl}(2,\mathbb C)\) and generalized \(q\)-Lauricella functions (Q1434798)

The reviewer [IMA J. Appl. Math. 30, 315--323 (1983; Zbl 0504.33003)] introduced a basic (or \(q\)-) extension \[ \Phi^{A: B';\dots; B^{(n)}}_{C: D';\dots; D^{(n)}} \] of the Srivastava-Daoust generalized hypergeometric series in \(n\) complex variables (the reviewer and \textit{M. C. Daoust} [Nederl. Akad. Wet., Proc., Ser. A 72, 449--457 (1969; Zbl 0185.29803)]; see also the reviewer and \textit{P. W. Karlsson} [Multiple Gaussian hypergeometric series (Wiley, New York) (1985; Zbl 0552.33001), especially see pp. 37 and 350]). Here, in the paper under review, the authors make use of a special case of the reviewer's multiple \(q\)-series in order to construct new \((m+ 1)\)-variable models of irreducible \(q\)-representations of Lie algebra \(\text{sl}(2, \mathbb{C})\) by applying techniques of fractional \(q\)-calculus in terms of \(q\)-derivative operators. Some interesting identities are also deduced.