×

A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture. (English) Zbl 0868.33009

Wave functions of the Calogero-Sutherland model can be expressed in terms of Jack polynomials. This note contains a Rodrigues-type formula for these polynomials where the creation operators appearing there are defined in terms of modified Dunkl operators. The authors use this formula to prove that all coefficients of the Jack polynomials are polynomials in the parameter \(\alpha\) with integral coefficients; this is part of a conjecture of I. Macdonald. A proof of the Rodrigues formula is given by the authors in [Commun. Math. Phys. 178, No. 2, 425-452 (1996; Zbl 0859.35103)].

MSC:

33C80 Connections of hypergeometric functions with groups and algebras, and related topics
33C70 Other hypergeometric functions and integrals in several variables
05E05 Symmetric functions and generalizations
81V70 Many-body theory; quantum Hall effect

Citations:

Zbl 0859.35103

Software:

LUC
PDF BibTeX XML Cite
Full Text: DOI arXiv