A q-analog of hypergeometric series well-poised in SU(n) and invariant G-functions (Q1071919)

We introduce natural q-analogs of hypergeometric series well-poised in SU(n), the related hypergeometric series in U(n), and invariant G-functions. We prove that both the SU(n) multiple q-sereis and the invariant G-functions satisfy general q-difference equations. Both the SU(N) and U(n) q-series are new multivariable generalizations of classical basic hypergeometric series of one variable. We prove an identity which expresses our U(n) multiple q-series as a finite sum of finite products of classical basic hypergeometric series. These U(n) q- sereis also satisfy an elegant reduction formula which is analogous to the ''inclusion lemma'' for classical invariant G-functions.