A classification of irreducible weakly spherical homogeneous spaces
type: Item
instance of: scholarly article
title: A classification of irreducible weakly spherical homogeneous spaces
zbMATH Open document ID: 1109.14035
author: Tatsuo Kimura
author: Daisuke Takeda
author: Tomohiro Kamiyoshi
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: The authors classify all homogeneous spaces \(\rho(H)|\text{GL}(V)\) with an open dense \(P\)-orbit, except when \(\text{GL}_1\times H,\,\Lambda_1\otimes\rho,\, V(1)\otimes V)\) is a trivial prehomogeneous vector space, where \(P\) is a proper parabolic subgroup of \(\text{GL}(V)\) and \(\rho: H\to \text{GL}(V)\) is a finite-dimensional irreducible representation of a semisimple algebraic group \(H\). When \(P\) is of type \(P(e_1,e_2,e_3)\), they classify all the cases up to equivalence. The classification is done over the complex number field.
reviewed by: Masanori Morishita
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 5078148
zbMATH Keywords: weakly spherical homogeneous spaces
zbMATH Keywords: irreducible prehomogeneous vector spaces
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2005.01.054
OpenAlex ID: W1979933267
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DOI: 10.1016/J.JALGEBRA.2005.01.054
description: scientific article; zbMATH DE number 5078148