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.
|Titolo:||Schubert Calculus on a Grassmann Algebra|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||10.4153/CMB-2009-023-x|
|Appare nelle tipologie:||1.1 Articolo in rivista|