Splitting the square of a Schur function into its symmetric and antisymmetric parts
type: Item
instance of: scholarly article
title: Splitting the square of a Schur function into its symmetric and antisymmetric parts
zbMATH Open document ID: 0853.05081
DOI: 10.1023/A:1022475927626
author: Christophe Carré
author: Bernard Leclerc
published in: Journal of Algebraic Combinatorics
publication date: 1996-12-09T00:00:00Z
review text: A new combinatorial description of the product of two Schur functions is considered. The key idea is to use domino tableaux (i.e. made up of \(1 \times 2\) rectangular boxes filled with integers increasing along the rows and strictly increasing along the columns) and to express the Littlewood-Richardson coefficients in terms of so-called Yamanouchi domino tableaux. In particular this approach gives a simple method of discriminating the tableaux in \(S_I S_I\) coming from symmetric parts \(S^2 (S_I)\). The \(q\)-analogues of the coefficients have also interesting combinatorial interpretations. It is shown that domino tableaux may be seen as the elements of a monoid, called the superplastic monoid. A new family of symmetric functions \((H\)-functions) are considered. The article is self-contained, has many examples and algorithms and can be used as a good introduction into the domino tableaux method.
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 773835
zbMATH Keywords: plethysm
zbMATH Keywords: Littlewood-Richardson rule
zbMATH Keywords: Schur functions
zbMATH Keywords: domino tableaux
zbMATH Keywords: Littlewood-Richardson coefficients
zbMATH Keywords: symmetric functions
reviewed by: Victor Ufnarovski
describes a project that uses: SYMMETRICA
MaRDI profile type: Publication
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full work available at URL: a:1022475927626
OpenAlex ID: W1585615506
description: scientific article; zbMATH DE number 773835