Schubert Calculus on a Grassmann Algebra

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The (classical, small quantum, equivariant) cohomology ring of the grassmannian G(k,n) is generated by certain derivations operating on an exterior algebra of a free module of rank n (Schubert Calculus on a Grassmann Algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. It also provides, by results of Laksov and Thorup, a presentation of the universal splitting algebra of a monic polynomial of degree n into the product of two monic polynomials, one of degree k.