A description based on Schubert classes of cohomology of flag manifolds

Masaki Nakagawa

doi:10.4064/fm199-3-5

A description based on Schubert classes of cohomology of flag manifolds

Research output: Contribution to journal › Article › peer-review

Abstract

We describe the integral cohomology rings of the flag manifolds of types B_n,D_n,G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.

Original language	English
Pages (from-to)	273-293
Number of pages	21
Journal	Fundamenta Mathematicae
Volume	199
Issue number	3
DOIs	https://doi.org/10.4064/fm199-3-5
Publication status	Published - 2008
Externally published	Yes

Keywords

Chow rings
Flag manifolds
Schubert calculus

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/fm199-3-5

Cite this

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AB - We describe the integral cohomology rings of the flag manifolds of types Bn,Dn,G2 and F4 in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.

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A description based on Schubert classes of cohomology of flag manifolds

Abstract

Keywords

ASJC Scopus subject areas

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