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A q-analog of hypergeometric series well-poised in SU(n) and invariant G-functions. (English) Zbl 0586.33014
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.
MSC:
33C80Connections of hypergeometric functions with groups and algebras
33C60Hypergeometric integrals and functions defined by them
33C05Classical hypergeometric functions, 2 F 1
22E70Applications of Lie groups to physics; explicit representations