A description based on Schubert classes of cohomology of flag manifolds
Volume 199 / 2008
Fundamenta Mathematicae 199 (2008), 273-293
MSC: Primary 57T15; Secondary 14M15.
DOI: 10.4064/fm199-3-5
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.
