Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials

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...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2016
Автор: Dunkl, C.F.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2016
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/147731
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 14 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147731
record_format dspace
spelling Dunkl, C.F.
2019-02-15T18:51:39Z
2019-02-15T18:51:39Z
2016
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 14 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 33C52; 42B10; 20C30; 46G10; 35F35
DOI:10.3842/SIGMA.2016.033
https://nasplib.isofts.kiev.ua/handle/123456789/147731
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.
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications. The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
spellingShingle Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
Dunkl, C.F.
title_short Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
title_full Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
title_fullStr Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
title_full_unstemmed Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
title_sort orthogonality measure on the torus for vector-valued jack polynomials
author Dunkl, C.F.
author_facet Dunkl, C.F.
publishDate 2016
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147731
citation_txt Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 14 назв. — англ.
work_keys_str_mv AT dunklcf orthogonalitymeasureonthetorusforvectorvaluedjackpolynomials
first_indexed 2025-11-30T11:39:43Z
last_indexed 2025-11-30T11:39:43Z
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