IJPAM: Volume 39, No. 2 (2007)

TOWARDS A PARSIMONIOUS CALCULATION
OF JACK POLYNOMIALS

Leigh Roberts
School of Economics and Finance
Victoria University
P.O. Box 600, Wellington, NEW ZEALAND
e-mail: leigh.roberts@vuw.ac.nz


Abstract.We prove the following new result concerning coefficients of expansions of Jack polynomials in monomial and elementary symmetric functions. Up to normalisation, we show that those coefficients are unchanged upon removing the first row or column of the Ferrers diagrams of the partitions used for indexing, or upon reflecting the Ferrers diagrams in a sufficiently large grid. Our results exhibit a strong duality between expansion of Jack polynomials in monomial and elementary symmetric functions; and provide an important step towards the efficient calculation of Jack polynomials through their parsimonious expansion in those symmetric functions.

Received: April 17, 2007

AMS Subject Classification: 05E05

Key Words and Phrases: Jack polynomials, monomial symmetric functions, elementary symmetric functions, Ferrers diagram

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 2