Schubert Calculus via Hasse-Schmidt Derivations
arXiv:math/0504293
Abstract
A natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian $G_k(\CC^n)$ as a ring of operators on the exterior algebra of a free module of rank . Classical Pieri's formula can be interpreted as Leibniz's rule enjoyed by special Schubert cycles with respect to the wedge product.
To appear on Asian Journal of Mathematics