Orbits of a maximal torus on a flag space
type: Item
instance of: scholarly article
title: Orbits of a maximal torus on a flag space
zbMATH Open document ID: 0581.14038
DOI: 10.1007/BF01086033
publication date: 1985-01-01T00:00:00Z
review text: Let G be a semisimple complex group, B be a Borel subgroup, X be the closure in G/B of a general orbit of a maximal torus. The author describes a basis of the homologies \(H_*(X,{\mathbb{Z}})\) and the image of the restriction homomorphism \(i^*: H^*(G/B,{\mathbb{Q}})\to H^*(X,{\mathbb{Q}})\). This image is the algebra of invariants \(H(X,{\mathbb{Q}})^ W\) with respect of the action induced by an action of the Weyl group W on X. There is an explicit presentation of generators and defining relations for this algebra of invariants. The \(i^*\)-images of the generalized Schubert cocycles are expressed in the terms of these generators. The note contains some applications to the case \(G=GL_ n\) and to usual Schubert cells.
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 3929181
zbMATH Keywords: orbits of a maximal torus on a flag space
zbMATH Keywords: basis of the homologies
zbMATH Keywords: algebra of invariants
zbMATH Keywords: Weyl group
zbMATH Keywords: generalized Schubert cocycles
zbMATH Keywords: Schubert cells
author: Alexander Klyachko
MaRDI profile type: Publication
cites work: Geometry in Grassmannians and a generalization of the dilogarithm
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3929181