Complexity and rank of homogeneous spaces
type: Item
instance of: scholarly article
title: Complexity and rank of homogeneous spaces
zbMATH Open document ID: 0706.14032
DOI: 10.1007/BF00181688
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: Let G be a connected reductive Lie group acting on an algebraic variety X and let \(B\supset T\) be a fixed Borel group and a maximal torus of G. The complexity of X, c(X), is defined to be the codimension of a generic B- orbit in X. Let \({\mathcal P}=\{f\in k(X)^*:\;bf=\lambda_ f(b),\quad b\in B\}\) where \(\lambda_ f\in {\mathfrak X}(B)\), the character group of B and let \(\Gamma\) (X) be the image of \(\lambda_ f\). \(\Gamma\) (X) is a free, finitely generated abelian group and the rank of \(\Gamma\) (X) is said to be the rank of X, r(X). The purpose of this paper is to study relations between c(X), r(X) and stabilizers of some actions of G and B. When X is a homogeneous space of G, the author obtains explicit formulas for the rank and complexity of quasiaffine G/H in terms of the co-isotropy representation of H.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 4158827
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: reductive Lie group
zbMATH Keywords: algebraic variety
zbMATH Keywords: complexity
zbMATH Keywords: rank
author: Dmitri I. Panyushev
reviewed by: Isabel Dotti Miatello
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181688
OpenAlex ID: W2063837444
description: scientific article; zbMATH DE number 4158827