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This article is cited in 3 scientific papers (total in 3 papers)
The Smallest Singular Values and Vector-Valued Jack Polynomials
Charles F. Dunkl Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville VA 22904-4137, USA
Abstract:
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.
Keywords:
nonsymmetric Jack polynomials; standard modules; Young tableaux.
Received: June 15, 2018; in final form October 22, 2018; Published online October 25, 2018
Citation:
Charles F. Dunkl, “The Smallest Singular Values and Vector-Valued Jack Polynomials”, SIGMA, 14 (2018), 115, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1414 https://www.mathnet.ru/eng/sigma/v14/p115
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Abstract page: | 118 | Full-text PDF : | 16 | References: | 24 |
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