Communications in Mathematical Physics

, Volume 210, Issue 2, pp 335–369 | Cite as

Formulas for q-Spherical Functions Using Inverse Scattering Theory of Reflectionless Jacobi Operators

  • J. F. van Diejen
  • A. N. Kirillov


We study the spectral problem associated to a Ruijsenaars-type (q-)difference version of the one-dimensional Schrödinger operator with Pöschl–Teller potential. The eigenfunctions are constructed explicitly with the aid of the inverse scattering theory of reflectionless Jacobi operators. As a result, we arrive at combinatorial formulas for basic hypergeometric deformations of zonal spherical functions on odd-dimensional hyperboloids and spheres.


Spectral Problem Spherical Function Inverse Scattering Scattering Theory Jacobi Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J. F. van Diejen
    • 1
  • A. N. Kirillov
    • 2
  1. 1.Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 1, Chile CL
  2. 2.Department of Mathematics, Hokkaido University, Sapporo 060-0810, JapanJP

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