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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 thedivided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As anapplication, we compute the Chow rings of the corresponding complex algebraicgroups, recovering thereby the results of R. Marlin.

A description based on Schubert classes of cohomology of flag manifolds