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. 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.

Schubert Calculus on a Grassmann Algebra / Gatto, Letterio; Santiago, T.. - In: CANADIAN MATHEMATICAL BULLETIN. - ISSN 0008-4395. - STAMPA. - 52:2(2009), pp. 200-212. [10.4153/CMB-2009-023-x]

Schubert Calculus on a Grassmann Algebra

GATTO, Letterio;
2009

Abstract

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. 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1503719
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