Schubert polynomials and skew Schur functions
type: Item
instance of: scholarly article
title: Schubert polynomials and skew Schur functions
zbMATH Open document ID: 0778.05082
DOI: 10.1016/0747-7171(92)90036-4
author: Axel Kohnert
published in: Journal of Symbolic Computation
publication date: 1993-01-16T00:00:00Z
review text: The author recalls the definitions of Schubert polynomials and successively introduces the skew Schur polynomials. They are defined as follows: let \(I=(i_ 1,\dots,i_ p)\) and \(J=(j_ 1,\dots,j_ p)\) be two \(p\)-tuples of integers such that \(0\leq i_ 1\leq\cdots\leq i_ p\), \(0\leq j_ 1\leq\cdots\leq j_ p\) and \(i_ k\leq j_ k\) for every \(k=1,\dots,p\). Then the skew Schur polynomial in the alphabet \(A_ n=\{a_ 1,\dots,a_ n\}\), \(S_{I/J}(A_ n)\), is the determinant of the matrix \((S_{j_ k+k-(j_ h+h)}(A_ n)_{h,k})\), where \(S_ m(A_ n)\) denotes the completely symmetric polynomial of degree \(m\) in the alphabet \(A_ n\). The author shows that any skew Schur polynomial is a restriction of a Schur polynomial. Finally, he shows an algorithm which computes a decomposition of a skew Schur function into a sum of Schur functions.
reviewed by: Alessandro Logar
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 96016
zbMATH Keywords: Schubert polynomials
zbMATH Keywords: skew Schur polynomial
zbMATH Keywords: Schur function
MaRDI profile type: Publication
full work available at URL: 0747-7171(92)90036-4
OpenAlex ID: W2020266863
cites work: Q3958580
cites work: Schubert polynomials and the Littlewood-Richardson rule
cites work: Q3947818
cites work: Flagged Schur functions, Schubert polynomials, and symmetrizing operators
description: scientific article; zbMATH DE number 96016