Permutation notations for the exceptional Weyl group \(F_4\).
type: Item
instance of: scholarly article
title: Permutation notations for the exceptional Weyl group \(F_4\).
zbMATH Open document ID: 1259.20056
author: Patricia Cahn
author: Ruth Haas
author: Aloysius G. Helminck
author: Jeremy Schwartz
author: Juan Li
published in: Involve
publication date: 2012-08-15T00:00:00Z
full work available at URL: p09.xhtml
review text: The root system \(\Phi\) of type \(F_4\) contains 24 short roots, say \(\Phi_1=\{\pm\alpha_i\mid 1\leqslant i\leqslant 12\}\). The Weyl group \(W\) of type \(F_4\) faithfully acts on the set \(\Phi_1\). Hence each element of \(W\) can be expressed as a signed permutation on the set \(X=\{1,2,\dots,12\}\). The paper describes the signed permutations on \(X\) corresponding to the elements of \(W\). A number of properties of such a presentation are discussed. A similar presentation is given for the Weyl group of type \(G_2\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 6066181
zbMATH Keywords: Weyl groups
zbMATH Keywords: Coxeter groups
zbMATH Keywords: one-line notations
zbMATH Keywords: signed permutations
MaRDI profile type: Publication
OpenAlex ID: W2041699698
DOI: 10.2140/INVOLVE.2012.5.81
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description: scientific article; zbMATH DE number 6066181