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

Haibao Duan, Xuezhi Zhao

Published 2008-01-16, updated 2015-02-08Version 12

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.