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

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Abstract:

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.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 1, Chile , , , , , , CL

    J. F. van Diejen

  2. Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan, , , , , , JP

    A. N. Kirillov

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  1. J. F. van Diejen
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  2. A. N. Kirillov
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Received: 24 November 1998 / Accepted: 14 September 1999

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van Diejen, J., Kirillov, A. Formulas for q-Spherical Functions Using Inverse Scattering Theory of Reflectionless Jacobi Operators. Comm Math Phys 210, 335–369 (2000). https://doi.org/10.1007/s002200050783

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  • DOI: https://doi.org/10.1007/s002200050783

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