A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• ISSN: 1815-0659
• Main Author: Dunkl, C.F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148638
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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 ca...