A Giambelli formula for isotropic Grassmannians

Details A Giambelli formula for isotropic Grassmannians A Giambelli formula for isotropic Grassmannians

2008-11-17

arxiv.org/abs/0811.2781v2

Mathematics

Algebraic Geometry

39 pages; improvements and corrections made to the exposition

Scientific paper

Let X be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in H^*(X,Z) as a polynomial in certain special Schubert classes. We study theta polynomials, a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on X. Furthermore, we prove that theta polynomials are special cases of Billey-Haiman Schubert polynomials and use this connection to express the former as positive linear combinations of products of Schur Q-functions and S-polynomials.

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