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An analytic formula for the \(A_2\) Jack polynomials. (English) Zbl 1193.33062

Summary: In this letter I shall review my joint results with V. B. Kuznetsov and E. K. Sklyanin [Indag. Math., New Ser. 14, No. 3–4, 451–482 (2003; Zbl 1057.33011)] on separation of variables (SoV) for the \(A_n\) Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919, 27–34 (1995)] where the integral representations for the \(A_2\) Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the \(A_2\) Jack polynomials in terms of generalized hypergeometric functions.

MSC:

33C52 Orthogonal polynomials and functions associated with root systems
05E05 Symmetric functions and generalizations
33C70 Other hypergeometric functions and integrals in several variables
81R12 Groups and algebras in quantum theory and relations with integrable systems
82B23 Exactly solvable models; Bethe ansatz

Citations:

Zbl 1057.33011
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