A Giambelli formula for even orthogonal Grassmannians

Details A Giambelli formula for even orthogonal Grassmannians A Giambelli formula for even orthogonal Grassmannians

2011-09-29

arxiv.org/abs/1109.6669v2

Mathematics

Algebraic Geometry

28 pages; added appendix gives geometric description of Schubert varieties, correcting errors in arXiv:0809.4966

Scientific paper

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.

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