On the structure of Jackson integrals of \(BC_n\) type and holonomic \(q\)-difference equations
type: Item
instance of: scholarly article
title: On the structure of Jackson integrals of \(BC_n\) type and holonomic \(q\)-difference equations
zbMATH Open document ID: 1155.33010
author: Kazuhiko Aomoto
author: Masahiko Ito
published in: Proceedings of the Japan Academy. Series A
publication date: 2008-08-12T00:00:00Z
review text: 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.
reviewed by: Jacques Sauloy
Mathematics Subject Classification ID: 33D67
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 5310503
zbMATH Keywords: Jackson integrals of \(BC_n\) type
zbMATH Keywords: \(q\)-de Rham cohomology of type \(BC_n\)
MaRDI profile type: Publication
full work available at URL: pjaa.81.145
OpenAlex ID: W2002682567
cites work: q-analogue of de Rham cohomology associated with Jackson integrals. II
cites work: Q4872757
cites work: Q4266194
cites work: BCn-type Jackson integral generalized from Gustafson'sCn-type sum
cites work: A determinant formula for a holonomic \(q\)-difference system associated with Jackson integrals of type \(BC_n\)
cites work: Q4693780
cites work: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
cites work: On certain multiple Bailey, Rogers and Dougall type summation formulas
cites work: Some q-Beta and Mellin-Barnes Integrals on Compact Lie Groups and Lie Algebras
cites work: Symmetry classification for Jackson integrals associated with irreducible reduced root systems
cites work: Q4805279
cites work: Askey-Wilson type integrals associated with root systems
cites work: \(q\)-difference shift for a \(BC_{n}\)-type Jackson integral arising from `elementary' symmetric polynomials
cites work: Another proof of Gustafson's \(C_n\)-type summation formula via `elementary' symmetric polynomials
cites work: A proof of the 𝑞-Macdonald-Morris conjecture for 𝐵𝐶_{𝑛}
cites work: Q3137252
DOI: 10.3792/PJAA.81.145
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description: scientific article; zbMATH DE number 5310503