An Analytic Formula for the A 2 Jack Polynomials 3 3 Separation of variables for Jack polynomials
نویسندگان
چکیده
In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451–482] on separation of variables (SoV) for the An Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27–34] where the integral representations for the A2 Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the A2 Jack polynomials in terms of generalised hypergeometric functions.
منابع مشابه
An Identity of Jack Polynomials
In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials
متن کاملAn Analytic Formula for the A 2 Jack Polynomials ⋆
Abstract. In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451–482] on separation of variables (SoV) for the An Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27–34] where the integral representations for the A2 Jack polynomials was derived. Using special polynomial bases I shall obtain a more ...
متن کاملA Normalization Formula for the Jack Polynomials in Superspace and an Identity on Partitions
We prove a conjecture of [3] giving a closed form formula for the norm of the Jack polynomials in superspace with respect to a certain scalar product. The proof is mainly combinatorial and relies on the explicit expression in terms of admissible tableaux of the non-symmetric Jack polynomials. In the final step of the proof appears an identity on weighted sums of partitions that we demonstrate u...
متن کاملar X iv : q - a lg / 9 60 80 20 v 1 2 3 A ug 1 99 6 SHIFTED JACK POLYNOMIALS , BINOMIAL FORMULA , AND APPLICATIONS
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [
متن کاملeb 2 00 4 Inversion of the Pieri formula for Macdonald polynomials
We give the explicit analytic development of Macdonald polynomials in terms of “modified complete” and elementary symmetric functions. These expansions are obtained by inverting the Pieri formula. Specialization yields similar developments for monomial, Jack and Hall–Littlewood symmetric functions. ∗The second author was fully supported by an APART fellowship of the Austrian Academy of Sciences...
متن کامل