By Borel's description the mod 2 cohomology algebra of the flag manifold is the polynomial algebra on the Stiefel-Whitney classes of canonical vector bundles modulo ideal generated by the dual classes. In the (special) case of Grassmann manifolds, a result by Jaworowski determines monomials in the Stiefel-Whitney that form an additive basis for the cohomology. I was wondering is there a similar result for (all) flag manifolds.
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