Quantum integrable systems and special functions
Mathematical Physics
2007-05-23 v1 math.MP
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 \kappa-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.
Cite
@article{arxiv.math-ph/0111021,
title = {Quantum integrable systems and special functions},
author = {A. M. Perelomov},
journal= {arXiv preprint arXiv:math-ph/0111021},
year = {2007}
}
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16 pages