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Schubert Calculus on a Grassmann Algebra

Published online by Cambridge University Press:  20 November 2018

Letterio Gatto
Dipartimento di Matematica, Politecnico di Torino, Duca degli Abruzzi, 24, 10129 Torino, Italy e-mail:
Taíse Santiago
Instituto de Matemática, Universidade Federal da Bahia, Av. Ademar Barros S/N, Ondina, Salvador-Bahia, 40170-110, (BA), Brazil e-mail:
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The (classical, small quantum, equivariant) cohomology ring of the grassmannian $G\left( k,\,n \right)$ is generated by certain derivations operating on an exterior algebra of a free module of rank $n$ (Schubert calculus on a Grassmann algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. Using results of Laksov and Thorup, it also provides a presentation of the universal factorization algebra of a monic polynomial of degree $n$ into the product of two monic polynomials, one of degree $k$.


Research Article
Copyright © Canadian Mathematical Society 2009


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