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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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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 |
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irk-123456789-1477312019-02-16T01:25:18Z Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials Dunkl, C.F. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147731 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Dunkl, C.F. |
| spellingShingle |
Dunkl, C.F. Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Dunkl, C.F. |
| author_sort |
Dunkl, C.F. |
| title |
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT dunklcf orthogonalitymeasureonthetorusforvectorvaluedjackpolynomials |
| first_indexed |
2023-05-20T17:28:10Z |
| last_indexed |
2023-05-20T17:28:10Z |
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1796153363637731328 |