Abstract
For an arbitrary complex (partial) flag manifold F, a Gröbner basis for the ideal which (in the Borel picture) determines the cohomology algebra H⁎(F;Z) is obtained. This Gröbner basis is used to derive multiplication rules for a convenient additive basis of H⁎(F;Z) given in terms of Chern classes of the canonical bundles over F. The analogous Gröbner bases related to the mod 2 cohomology of real flag manifolds are also presented.
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