Operator identities and several U(n+1) generalizations of the Kalnins–Miller transformations

Multiple basic hypergeometric series associated to the unitary group U(n+1) have been investigated by various authors. Many different types of such series exist in the literature. From several U(n+1) generalizations of q-Chu–Vandermonde summation theorem established by Milne [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93–187], the purpose of this paper is to obtain several U(n+1) generalizations of the Kalnins–Miller transformation by applying the q-exponential operator technique.