The Smallest Singular Values and Vector-Valued Jack Polynomials

Symmetry Integrability and Geometry-Methods and Applications

article

Charles F. Dunkl¹ 

[1] Department of Mathematics, University of Virginia

关键词: nonsymmetric Jack polynomials;    standard modules;    Young tableaux;   

DOI  :  10.3842/SIGMA.2018.115

来源: National Academy of Science of Ukraine

【 摘 要 】

There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for the smallest singular values are constructed in terms of the Jack polynomials. The smallest singular values bound the region of positivity of the bilinear symmetric form for which the Jack polynomials are mutually orthogonal. As background there are some results about general finite reflection groups and singular values in the context of standard modules of the rational Cherednik algebra.

【 授权许可】

Unknown