Schubert presentation of the integral cohomology ring of the flag manifolds G/T

TL;DR

This paper provides a canonical presentation of the integral cohomology ring of complete flag manifolds G/T for compact Lie groups G, advancing Schubert calculus methods and their applications in topology.

Contribution

It introduces a new canonical presentation of H^{ ext{*}}(G/T), facilitating computations in Schubert calculus and applications to cohomology of Lie groups.

Findings

Canonical presentation of H^{*}(G/T) established

Applied to compute H^{*}(G) via Schubert classes

Determined mod p cohomology structure as a Hopf algebra

Abstract

Let G be a compact connected Lie group with a maximal torus T\subsetG. In the context of Schubert calculus we obtain a canonical presentation for the integral cohomology ring H^{\ast}(G/T) of the complete flag manifold G/T. The result have been applied in [15] to construct the integral cohomology ring H^{\ast}(G) in terms of Schubert classes on G/T, and in [16] to determine the structure of the modp cohomology H^{\ast}(G;F_{p}) as a Hopf algebra over the Steenrod algebra.