Cycles de Schubert et cohomologie équivariante de K/T. (Schubert cycles and equivariant cohomology of K/T)
type: Item
instance of: scholarly article
title: Cycles de Schubert et cohomologie équivariante de K/T. (Schubert cycles and equivariant cohomology of K/T)
zbMATH Open document ID: 0624.22005
DOI: 10.1007/BF01388791
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143358
review text: Let K be a compact connected Lie group, T be a maximal torus in K and T' be its normalizer in K. The flag variety \(X=K/T\) admits a cellular decomposition \(X=\cup X_ w\) with cells indexed by all elements w of the Weyl group \(W=T'/T\). The closures \(\bar X{}_ w\) of these cells determine elements in the dual space to the complex cohomology space \(H^*(X)\) that are called Schubert cycles. The aim of the present paper is to define and to study the analogues of Schubert cycles for the equivariant cohomology \(H^*_ K(X)\). Identifying (by the Chern-Weil isomorphism) \(H^*_ K(X)\) with the space of polynomial functions on the Lie algebra \({\mathfrak t}\) of T the author gives an explicit formula for the equivariant Schubert cycles in terms of the reduced decompositions of elements of W.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 55N25
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 4012917
zbMATH Keywords: polynomial functions on Lie algebra
zbMATH Keywords: compact connected Lie group
zbMATH Keywords: maximal torus
zbMATH Keywords: flag variety
zbMATH Keywords: cellular decomposition
zbMATH Keywords: Weyl group
zbMATH Keywords: Schubert cycles
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: reduced decompositions
author: Alberto Arabia
reviewed by: Sergei Gelfand
MaRDI profile type: Publication
cites work: Q3723355
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description: scientific article; zbMATH DE number 4012917