Determinantal expression and recursion for Jack polynomials
type: Item
instance of: scholarly article
title: Determinantal expression and recursion for Jack polynomials
zbMATH Open document ID: 0934.05123
author: Luc Lapointe
author: J. Morse
author: Alain Lascoux
published in: The Electronic Journal of Combinatorics
publication date: 2000-02-17T00:00:00Z
full work available at URL: https://eudml.org/doc/120183
full work available at URL: v7i1n1.html
review text: The Jack polynomials \(J_{\lambda}[x_1,\ldots,x_N;\alpha]\) form a basis for the space of symmetric polynomials in \(N\) variables; the specialization \(\alpha=1\) in \(J_{\lambda}[x;\alpha]\) gives the Schur function \(s_{\lambda}[x]\). The main purpose of the paper under review is to give a matrix with determinant equal to \(J_{\lambda}[x;\alpha]\). The matrix under consideration has only one nonzero subdiagonal. This gives rise to a simple recursion which may be used for the rapid computation of Jack polynomials. As a consequence of these results the authors obtain a new determinantal form for the Schur functions and a recursion for the Kostka numbers which express the coefficients of the Schur functions in terms of the monomial basis. The authors illuminate their results with successfully selected examples.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 1402581
zbMATH Keywords: symmetric functions
zbMATH Keywords: Schur functions
zbMATH Keywords: Jack polynomials
zbMATH Keywords: Kostka numbers
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1402581