A description based on Schubert classes of cohomology of flag manifolds

TL;DR

This paper describes the integral cohomology rings of certain flag manifolds using Schubert classes and divided difference operators, and applies these results to compute Chow rings of related algebraic groups.

Contribution

It provides a new description of cohomology rings of specific flag manifolds using Schubert classes and operators, extending previous results to types B_n, D_n, G_2, and F_4.

Findings

Cohomology rings expressed in terms of Schubert classes

Computed Chow rings of complex algebraic groups

Extended results to additional Lie types

Abstract

We describe the integral cohomology rings of the flag manifolds of types B_n, D_n, G_2 and F_4 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.