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Quantum integrable systems and special functions

A. M. Perelomov
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Abstract

The wave functions of quantum Calogero-Sutherland systems for trigonometric case are related to polynomials in l variables (l is a rank of root system) and they are the generalization of Gegenbauer polynomials and Jack polynomials. Using the technique of κ-deformation of Clebsch-Gordan series developed in previous authors papers we investigate some new properties of generalized Gegenbauer polynomials.Note that similar results are also valid in A_2 case for more general two-parameter deformation ((q,t)-deformation) introduced by Macdonald.

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A. M. Perelomov. 2001-11-12. Quantum integrable systems and special functions. https://arxiv.org/abs/math-ph/0111021

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