A Giambelli formula for even orthogonal Grassmannians

Let be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in the classical and quantum cohomology rings of as a polynomial in certain s...

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Bibliographic Details
Published in:Journal für die reine und angewandte Mathematik 2015-11, Vol.2015 (708), p.17-48
Main Authors: Buch, Anders Skovsted, Kresch, Andrew, Tamvakis, Harry
Format: Article
Language:English
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Summary:Let be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in the classical and quantum cohomology rings of as a polynomial in certain special Schubert classes. Our analysis reveals a surprising relation between the Schubert calculus on even and odd orthogonal Grassmannians. We also study , a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on .
ISSN:0075-4102
1435-5345
DOI:10.1515/crelle-2013-0071