Orthogonality measure on the torus for vector-valued Jack polynomials

DOI10.3842/SIGMA.2016.033zbMath1338.33024arXiv1511.06721MaRDI QIDQ274867

Charles F. Dunkl

Publication date: 25 April 2016

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.06721

zbMATH Keywords

Fourier-Stieltjes coefficientsmatrix-valued measurenonsymmetric Jack polynomialssymmetric group modules

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Vector-valued measures and integration (46G10) Orthogonal polynomials and functions associated with root systems (33C52) Systems of linear first-order PDEs (35F35)

Related Items (3)

The smallest singular values and vector-valued Jack polynomials ⋮ A linear system of differential equations related to vector-valued Jack polynomials on the torus ⋮ The Dunkl weight function for rational Cherednik algebras

Cites Work

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• Symmetric and antisymmetric vector-valued Jack polynomials
• A new construction of Young's seminormal representation of the symmetric groups
• Differential-difference operators and monodromy representations of Hecke algebras
• Harmonic analysis for certain representations of graded Hecke algebras
• Exact operator solution of the Calogero-Sutherland model
• Vector polynomials and a matrix weight associated to dihedral groups
• Orthogonal functions generalizing Jack polynomials
• Certain Hypergeometric Series Related to the Root System BC
• Unitary representations of rational Cherednik algebras
• Orthogonal Polynomials of Several Variables
• A New Approach to the Representation Theory of the Symmetric Groups. II

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