Visible actions on flag varieties of type C and a generalization of the Cartan decomposition
type: Item
instance of: scholarly article
title: Visible actions on flag varieties of type C and a generalization of the Cartan decomposition
zbMATH Open document ID: 1277.22014
author: Yuichiro Tanaka
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2013-10-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tmj/1372182727
review text: Let \(G\) be a connected compact simple Lie group of type \(C\), \(K\) a Chevalley-Weyl involution-fixed point subgroup and \(L,H\) Levi subgroups. The goal of present paper is to classify all the pairs \((L,H)\) such that \(G=LKH\). It is proved that this last relation holds if and only if 1) \((G,H)\) and \((G,L)\) are both symmetric pairs, or 2) \(L\) is a Levi subgroup of maximal dimension and \(H\) is an arbitrary maximal Levi subgroup up to switch of \(L,H\). An application to multiplicity-free theorems of representations is also discussed.
reviewed by: Panagiotis Batakidis
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 32A37
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 6214260
zbMATH Keywords: Cartan decomposition
zbMATH Keywords: multiplicity-free representation
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: flag variety
zbMATH Keywords: visible action
zbMATH Keywords: herringbone stitch
MaRDI profile type: Publication
OpenAlex ID: W2061973420
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DOI: 10.2748/TMJ/1372182727
description: scientific article; zbMATH DE number 6214260