\(q\)-gamma and \(q\)-beta functions in quantum algebra representation theory
The authors consider a Hopf algebra \(\mathcal G_q\) which is generated by two generators. It is a \(q\)-deformation of the algebra of the infinitesimal affine transformations of the oriented line. By studying \(q\)-exponentials of the generators in some representations of \(\mathcal G_q\), the authors derive a number of identities featuring \(q\)-gamma and \(q\)-beta functions, and ordinary and bilateral basic hypergeometric series.
scientific article; zbMATH DE number 908384
scientific article