Annals of Combinatorics 3 (1999) 159-170

Symmetric Jack Polynomials from Non-Symmetric Theory

T.H. Baker and P.J. Forrester

Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia
{tbaker, matpjf}

Received Feburary 25, 1999

AMS Subject Classification: 33C80

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 non-symmetric 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.

Keywords: Jack polynomials, symmetric functions


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