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September 2005 Schubert Calculus via Hasse-Schmidt Derivations
Letterio Gatto
Asian J. Math. 9(3): 315-322 (September 2005).

Abstract

A natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian $G_k(\mathbb{C}^n)$ 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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Letterio Gatto. "Schubert Calculus via Hasse-Schmidt Derivations." Asian J. Math. 9 (3) 315 - 322, September 2005.

Information

Published: September 2005
First available in Project Euclid: 3 May 2006

zbMATH: 1099.14045
MathSciNet: MR2214955

Rights: Copyright © 2005 International Press of Boston

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Vol.9 • No. 3 • September 2005
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