Schubert Calculus via Hasse-Schmidt Derivations

Letterio Gatto

doi:ajm/1146673623

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Home > Journals > Asian J. Math. > Volume 9 > Issue 3 > Article

September 2005 Schubert Calculus via Hasse-Schmidt Derivations

Letterio Gatto

Asian J. Math. 9(3): 315-322 (September 2005).

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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.