The product of a nonsymmetric jack polynomial with a linear function

Dan Marshall

doi:10.1090/s0002-9939-02-06716-3

The product of a nonsymmetric jack polynomial with a linear function

Dan Marshall^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper a decomposition in terms of the nonsymmetric Jack polynomials is given for the product of any nonsymmetric Jack polynomial E_η(z) with z_i. This decomposition generalises a recurrence formula satisfied by single variable orthogonal polynomials on the unit circle. The decomposition also allows the evaluation of the generalised binomial coefficients (_ν^η) associated with the nonsymmetric Jack polynomials for |η| = |ν| + 1.

Original language	English
Pages (from-to)	1817-1827
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	6
DOIs	https://doi.org/10.1090/s0002-9939-02-06716-3
Publication status	Published - Jun 2003

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title = "The product of a nonsymmetric jack polynomial with a linear function",

abstract = "In this paper a decomposition in terms of the nonsymmetric Jack polynomials is given for the product of any nonsymmetric Jack polynomial Eη(z) with zi. This decomposition generalises a recurrence formula satisfied by single variable orthogonal polynomials on the unit circle. The decomposition also allows the evaluation of the generalised binomial coefficients (νη) associated with the nonsymmetric Jack polynomials for |η| = |ν| + 1.",

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AB - In this paper a decomposition in terms of the nonsymmetric Jack polynomials is given for the product of any nonsymmetric Jack polynomial Eη(z) with zi. This decomposition generalises a recurrence formula satisfied by single variable orthogonal polynomials on the unit circle. The decomposition also allows the evaluation of the generalised binomial coefficients (νη) associated with the nonsymmetric Jack polynomials for |η| = |ν| + 1.

KW - Generalized binomial coefficients

KW - Jack polynomials

KW - Pieri formula

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DO - 10.1090/s0002-9939-02-06716-3

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EP - 1827

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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The product of a nonsymmetric jack polynomial with a linear function

Abstract

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