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On the structure of Jackson integrals of \(BC_n\) type and holonomic \(q\)-difference equations. (English) Zbl 1155.33010

The authors study a particular \(q\)-analogue of de Rham cohomology complex related to so-called Jackson integrals; the latter are actually by definition sums over multiplicative lattices in \((\mathbb{C}^{*})^{n}\). In the case of Jackson integrals of type \(BC_n\), the paper studies separately symmetric and non-symmetric cohomologies, giving explicit bases. Last, it is proved that these integrals satisfy holonomic systems of linear \(q\)-difference equations with respect to the parameters.

MSC:

33D67 Basic hypergeometric functions associated with root systems
39A12 Discrete version of topics in analysis
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