ar X iv : q - a lg / 9 61 20 14 v 1 1 1 D ec 1 99 6 Integral soluitons of q - difference equations

ar X iv : m at h / 99 12 14 0 v 1 [ m at h . C A ] 1 7 D ec 1 99 9 THE ASKEY - WILSON FUNCTION TRANSFORM SCHEME

In this paper we present an addition to Askey’s scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and Bessel function. The generalised orthogonality relations and the second order q-difference equations for these families are given. Limit transitions between the...

ar X iv : q - a lg / 9 61 20 03 v 1 1 D ec 1 99 6 Non – Symmetric Jack Polynomials and Integral Kernels

We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange terms. For the non-symmetric Jack polynomials, the constant term normalization N η is evaluated using recurrence relations, and N η is related to the norm for the non-symmetric analogue of the power-s...

ar X iv : q - a lg / 9 41 20 06 v 1 1 9 D ec 1 99 4 CLASSICAL SPINOR STRUCTURES ON QUANTUM SPACES

A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular, analogs of the Dirac operator and the Laplacian are introduced and analyzed. A general construction of examples of quantum spaces with a spinor structure is presented.

ar X iv : q - a lg / 9 51 10 09 v 2 1 7 D ec 1 99 5 h - deformation of GL ( 1 | 1 )

h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.

ar X iv : q - a lg / 9 70 90 01 v 1 1 S ep 1 99 7 Bilinear identity for q - hypergeometric integrals