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Symmetric Jack polynomials from non-symmetric theory

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Abstract

We show how a number of fundamental properties of the symmetric and anti-symmetric Jack polynomials can be derived from knowledge of the corresponding properties of the nonsymmetric Jack polynomials. These properties include orthogonality relations, normalization formulas, a specialization formula and the evaluation of a proportionality constant relating the anti-symmetric Jack polynomials to a product of differences multiplied by the symmetric Jack polynomials with a shifted parameter.

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Author notes

  1. T. H. Baker

    Present address: RIMS, Kyoto University, 606, Kyoto, Japan

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, 3052, Parkville, Victoria, Australia

    T. H. Baker & P. J. Forrester

Authors
  1. T. H. Baker
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  2. P. J. Forrester
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Additional information

This work was supported by the Australian Research Council.

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Baker, T.H., Forrester, P.J. Symmetric Jack polynomials from non-symmetric theory. Annals of Combinatorics 3, 159–170 (1999). https://doi.org/10.1007/BF01608781

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  • DOI: https://doi.org/10.1007/BF01608781

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