Creation operators for the Macdonald and Jack polynomials
type: Item
instance of: scholarly article
title: Creation operators for the Macdonald and Jack polynomials
zbMATH Open document ID: 0882.33010
DOI: 10.1023/A:1007332315944
author: Luc Lapointe
author: Luc Vinet
published in: Letters in Mathematical Physics
publication date: 1998-02-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/q-alg/9607024
review text: In a previous paper [\textit{L. Lapointe} and \textit{L. Vinet} in Int. Math. Res. 1995, No. 9, 419-424 (1995; Zbl 0868.33009)] the authors constructed Jack polynomials by means of creation operators acting on the identity. Since Jack polynomials are a specialization of Macdonald polynomials, a similar problem is considered here. A Rodrigues-type formula is derived, expressing a Macdonald polynomial as a string of creation operators acting on the identity. The present construction is however different from the one for Jack polynomials. In terms of the creation operators some conjectures are formulated which imply that the expansion coefficients of the Macdonald polynomials in the monomial basis are polynomials with integer coefficients.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 1043138
zbMATH Keywords: Macdonald polynomials
zbMATH Keywords: symmetric functions
zbMATH Keywords: Rodrigues formula
MaRDI profile type: Publication
arXiv ID: q-alg/9607024
OpenAlex ID: W2998900270
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description: scientific article