Schubert Calculus on a Grassmann Algebra

http://dx.doi.org/10.4153/CMB-2009-023-x
Canad. Math. Bull. 52(2009), 200-212

  Published:2009-06-01
 Printed: Jun 2009

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 $k$.