Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
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| Creator |
Dunkl, C.F.
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| 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.
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| Date |
2019-02-15T18:51:39Z
2019-02-15T18:51:39Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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