An infinitesimal characterization of the complexity of homogeneous spaces
type: Item
instance of: scholarly article
title: An infinitesimal characterization of the complexity of homogeneous spaces
zbMATH Open document ID: 0940.14037
DOI: 10.1007/BF01236663
author: Dmitri I. Panyushev
author: È. B. Vinberg
published in: Transformation Groups
publication date: 1999-06-15T00:00:00Z
review text: The complexity of a homogeneous space \(O\) of a connected reductive group \(G\) is the minimal codimension of the orbits of a Borel subgroup \(B \subset G\) in \(O\). The authors express this complexity in terms of the relative position of the Lie algebra of the stabilizer of a generic point of \(O\) and the \(-1\)-eigenspace of a Weil involution of \(\theta\) of the Lie algebra of \(G\). A basic tool of the proof is the doubled action of \(G\) on \(O \times O\) defined by \(\theta\). Here previous work of the first author plays a central rôle.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1286200
zbMATH Keywords: complexity of homogeneous spaces
zbMATH Keywords: reductive groups
zbMATH Keywords: Weil involution
reviewed by: Jürgen Hausen
MaRDI profile type: Publication
cites work: Weakly symmetric spaces and spherical varieties
cites work: Complexity and rank of homogeneous spaces
cites work: A restriction theorem and the Poincaré series for \(U\)-invariants
cites work: Reductive group actions on affine varieties and their doubling
full work available at URL: https://doi.org/10.1007/bf01236663
OpenAlex ID: W2003510537
description: scientific article; zbMATH DE number 1286200