A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus
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| Creator |
Dunkl, C.F.
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| Description |
For each irreducible module of the symmetric group SN 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 two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N-torus. The latter is valid for the parameter lying in an interval about zero which depends on the module. The author in a previous paper [SIGMA 12 (2016), 033, 27 pages] proved the existence of the measure and that its absolutely continuous part satisfies a system of linear differential equations. In this paper the system is analyzed in detail. The N-torus is divided into (N−1)! connected components by the hyperplanes xi=xj, i
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| Date |
2019-02-18T16:50:12Z
2019-02-18T16:50:12Z 2017 |
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| Type |
Article
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| Identifier |
A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus / C.F. Dunkl // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 11 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33C52; 32W50; 35F35; 20C30; 42B05 DOI:10.3842/SIGMA.2017.040 http://dspace.nbuv.gov.ua/handle/123456789/148638 |
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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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