Strongly orthogonal subsets in root systems
type: Item
instance of: scholarly article
title: Strongly orthogonal subsets in root systems
zbMATH Open document ID: 1026.17010
author: Yoshio Agaoka
author: Eiji Kaneda
published in: Hokkaido Mathematical Journal
publication date: 2003-12-08T00:00:00Z
review text: A subset \(\Gamma\) of a finite root system \(\Delta\) is called strongly orthogonal (SOS) if when \(\alpha, \beta \in \Gamma\), \(\alpha \neq \beta\), then \(\alpha \pm \beta \not \in \Delta \cup \{0\}\). Such \(\Gamma\) occur in problems involving symmetric spaces. Two SOS of \(\Delta\) are equivalent if an element of the Weyl group of \(\Delta\) takes one to the other. The authors classify the maximal SOS (MSOS) and find the number of equivalences classes of MSOS. This number is \(1\) if \(\Delta=A_n\), \(B_n\) (\(n\) odd), \(D_n\), \(E_n\) or \(G_2\). It is \(2\) if \(\Delta=B_n\) (\(n\) even) or \(F_4\). It is \([n/2]+1\) if \(\Delta=C_n\) and is \(n+1\) if \(\Delta=BC_n\).
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 1751375
zbMATH Keywords: strongly orthogonal root system
reviewed by: Ernest L. Stitzinger
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350911773
OpenAlex ID: W2045360332
Wikidata QID: Q61908554
DOI: 10.14492/HOKMJ/1350911773
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description: scientific article; zbMATH DE number 1751375