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arXiv · 1109.6669

A Giambelli formula for even orthogonal Grassmannians

Anders S. Buch·Andrew Kresch·Harry Tamvakis
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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.

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Anders S. Buch, Andrew Kresch, Harry Tamvakis. 2012-03-29. A Giambelli formula for even orthogonal Grassmannians. https://arxiv.org/abs/1109.6669

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