Quantum integrable systems and special functions

2001/11/12 by A. M. Perelomov, Perelomov, A. M.
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0111021

16 pages

arxiv created 2001/11/12 · openalex publication_date 2001/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 A₂ case for more general two-parameter deformation ((q,t)-deformation) introduced by Macdonald.

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