Schubert Calculus on a Grassmann Algebra

Gatto, Letterio ; Santiago, Taíse

Canadian mathematical bulletin, Tome 52 (2009) no. 2, pp. 200-212

Résumé

The (classical, small quantum, equivariant) cohomology ring of the grassmannian $G\left( k,\,n \right)$ 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 $k$ .

Détail

DOI : 10.4153/CMB-2009-023-x

Mots-clés : 14N15, 14M15

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