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Zbl 0586.33014
Milne, S.C.
A q-analog of hypergeometric series well-poised in SU(n) and invariant G-functions. (English)
[J] Adv. Math. 58, 1-60 (1985). ISSN 0001-8708

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 2000:: *33C80 Connections of theory of special functions with groups and algebras
33C60 Hypergeometric integrals and functions defined by them
33C05 Classical hypergeometric functions
22E70 Appl. of Lie groups to physics

Keywords: q-analogs of hypergeometric series well-poised in SU(n); invariant G- functions; SU(n) multiple q-sereis; U(n) multiple q-series

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