Asian Journal of Mathematics

Volume 9 (2005)

Number 3

Schubert Calculus via Hasse-Schmidt Derivations

Pages: 315 – 322

DOI: http://dx.doi.org/10.4310/AJM.2005.v9.n3.a2

Author

Letterio Gatto

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.

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