A Giambelli formula for even orthogonal Grassmannians
Algebraic Geometry
2012-04-02 v2
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 singular and quantum cohomology ring 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.
Cite
@article{arxiv.1109.6669,
title = {A Giambelli formula for even orthogonal Grassmannians},
author = {Anders S. Buch and Andrew Kresch and Harry Tamvakis},
journal= {arXiv preprint arXiv:1109.6669},
year = {2012}
}
Comments
28 pages; added appendix gives geometric description of Schubert varieties, correcting errors in arXiv:0809.4966