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Schubert Calculus on a Grassmann Algebra

 Printed: Jun 2009
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The ({\em classical}, {\em small quantum}, {\em 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. Using results of Laksov and Thorup, it also provides a presentation of the universal factorization algebra of a monic polynomial of degree $n$ into the product of two monic polynomials, one of degree $k$.
MSC Classifications: 14N15, 14M15 show english descriptions Classical problems, Schubert calculus
Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
14N15 - Classical problems, Schubert calculus
14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

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