Schubert Calculus via Hasse-Schmidt Derivations
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 $n$. Classical Pieri's formula can be interpreted as Leibniz's rule enjoyed by special Schubert cycles with respect to the wedge product.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- April 2005
- DOI:
- 10.48550/arXiv.math/0504293
- arXiv:
- arXiv:math/0504293
- Bibcode:
- 2005math......4293G
- Keywords:
-
- Algebraic Geometry;
- 14M15;
- 14N15
- E-Print:
- To appear on Asian Journal of Mathematics