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Schubert Calculus on a Grassmann Algebra

Published online by Cambridge University Press:  20 November 2018

Letterio Gatto  and
Taíse Santiago
Letterio Gatto
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi, 24, 10129 Torino, Italy e-mail: [email protected]
Taíse Santiago
Affiliation:
Instituto de Matemática, Universidade Federal da Bahia, Av. Ademar Barros S/N, Ondina, Salvador-Bahia, 40170-110, (BA), Brazil e-mail: [email protected]
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Abstract

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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 $k$.

Keywords

14N1514M15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 2 , 01 June 2009 , pp. 200 - 212
Copyright
Copyright © Canadian Mathematical Society 2009

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