Connection formula of symmetric \(A\)-type Jackson integrals
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.
scientific article; zbMATH DE number 624874