Connection formula of symmetric \(A\)-type Jackson integrals
type: Item
instance of: scholarly article
title: Connection formula of symmetric \(A\)-type Jackson integrals
zbMATH Open document ID: 0802.33016
DOI: 10.1215/S0012-7094-94-07406-1
author: Kazuhiko Aomoto
author: Yoshifumi Kato
published in: Duke Mathematical Journal
publication date: 1994-08-25T00:00:00Z
review text: The connection problem of Jackson integrals for higher-dimensional cases is investigated. Let \(\overline{X}\) be an algebraic torus of dimension \(n\) whose coordinates are \(t= (t_ 1,\dots, t_ n)\) and \(X\) an integral lattice of \(\overline{X}\) which acts on \(\overline{X}\) by multiplication. The Jackson integral is defined as an integral, over \(X\) orbits, of functions \(f(t)\) on \(\overline{X}\). Then, the connection coefficients among the Jackson integrals over special \(X\) orbits are determined. A fundamental theorem which shows the properties of the regularized Jackson integrals is proven for arbitrary dimension \(n\). Some remarks about the graphs associated to the model and the connection coefficients are also given.
Mathematics Subject Classification ID: 33C80
zbMATH DE Number: 624874
zbMATH Keywords: Jackson integrals
zbMATH Keywords: algebraic torus
zbMATH Keywords: lattice
zbMATH Keywords: orbits
zbMATH Keywords: graphs
zbMATH Keywords: connection coefficients
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 624874