An algebraic formula for the Gysin homomorphism from G/B to G/P
type: Item
instance of: scholarly article
title: An algebraic formula for the Gysin homomorphism from G/B to G/P
zbMATH Open document ID: 0629.57030
author: Ersan Akyildiz
author: James B. Carrell
published in: Illinois Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let G be linear, semisimple algebraic group, with Borel subgroup B, containing a maximal torus H. If P is a parabolic subgroup containing B, there is a natural projection map \(\pi\) : G/B\(\to G/P\) as well as a Gysin homomorphism (or transfer) \(\pi_*: H^*(G/B; {\mathbb{C}})\to H^*(G/P; {\mathbb{C}}).\) The principal goal of this paper is to derive an algebraic formula for \(\pi_*\). If h is the Lie algebra of H, R is the graded, symmetric algebra of \(h^*\), which admits a natural action of the Weyl group W. The authors succeed in describing \(\pi_*\) in terms of quotients of R and related algebras. The methods involve the calculation of the residues of the zeros of holomorphic vector fields and are quite technical.
Mathematics Subject Classification ID: 57T15
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 4024330
zbMATH Keywords: linear, semisimple algebraic
zbMATH Keywords: Borel subgroup
zbMATH Keywords: parabolic subgroup
zbMATH Keywords: Gysin homomorphism
zbMATH Keywords: residues of the zeros of holomorphic vector fields
reviewed by: Donald W. Kahn
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4024330