Summary
Two sets of generators of the cohomology ring of a complex (incomplete) flag manifold are obtained in terms of Ehresmann classes. Intersection formulae of the bases elements with any Ehresmann class are then given, thus determining the ring structure of the cohomology ring.
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Ilori, S.A. Intersection formulae in flag manifolds. Annali di Matematica pura ed applicata 127, 307–319 (1981). https://doi.org/10.1007/BF01811728
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DOI: https://doi.org/10.1007/BF01811728