A formula for Jack polynomials of the second order
نویسندگان
چکیده
منابع مشابه
An 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 Recursion and a Combinatorial Formula for Jack Polynomials
The Jack polynomials Jλ(x; α) form a remarkable class of symmetric polynomials. They are indexed by a partition λ and depend on a parameter α. One of their properties is that several classical families of symmetric functions can be obtained by specializing α, e.g., the monomial symmetric functions mλ (α = ∞), the elementary functions eλ′ (α = 0), the Schur functions sλ (α = 1) and finally the t...
متن کاملAn Analytic Formula for the A 2 Jack Polynomials 3 3 Separation of variables for Jack polynomials
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 e...
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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 [ x i ( xi ∂ ∂xi + (n− j)θ + u )]
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In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials
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ژورنال
عنوان ژورنال: Applicationes Mathematicae
سال: 2007
ISSN: 1233-7234,1730-6280
DOI: 10.4064/am34-1-9