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A Giambelli formula for even orthogonal Grassmannians


Skovsted Buch, Anders; Kresch, Andrew; Tamvakis, Harry (2015). A Giambelli formula for even orthogonal Grassmannians. Journal für die Reine und Angewandte Mathematik, 2015(708):17-48.

Abstract

Let X 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 X 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 eta polynomials, a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on X.

Abstract

Let X 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 X 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 eta polynomials, a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on X.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:September 2015
Deposited On:14 Jan 2016 11:58
Last Modified:05 Apr 2016 19:16
Publisher:De Gruyter
ISSN:0075-4102
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1515/crelle-2013-0071

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