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Schubert Calculus via Hasse-Schmidt Derivations

Letterio Gatto
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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 $G_k(\CC^n)$ 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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Letterio Gatto. 2005-04-14. Schubert Calculus via Hasse-Schmidt Derivations. https://arxiv.org/abs/math/0504293

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