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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
Charles F. Dunkl Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville VA 22904-4137, USA
Аннотация:
For each irreducible module of the symmetric group on $N$ objects there is a set of parametrized nonsymmetric Jack polynomials in $N$ variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to certain Hermitian forms. These polynomials were studied by the author and J.-G. Luque using a Yang–Baxter graph technique. This paper constructs a matrix-valued measure on the $N$-torus for which the polynomials are mutually orthogonal. The construction uses Fourier analysis techniques. Recursion relations for the Fourier–Stieltjes coefficients of the measure are established, and used to identify parameter values for which the construction fails. It is shown that the absolutely continuous part of the measure satisfies a first-order system of differential equations.
Ключевые слова:
nonsymmetric Jack polynomials; Fourier–Stieltjes coefficients; matrix-valued measure; symmetric group modules.
Поступила: 26 ноября 2015 г.; в окончательном варианте 23 марта 2016 г.; опубликована 27 марта 2016 г.
Образец цитирования:
Charles F. Dunkl, “Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials”, SIGMA, 12 (2016), 033, 27 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1115 https://www.mathnet.ru/rus/sigma/v12/p33
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