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A Giambelli formula for isotropic Grassmannians

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arxiv 0811.2781 v2 pith:ICISWDLC submitted 2008-11-17 math.AG

Anders S. Buch , Andrew Kresch , Harry Tamvakis This is my paper · ORCID
classification math.AG
keywords polynomialsschubertformulagiambelliisotropicprovespecialtheta
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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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  1. Schubert defects in Lagrangian Grassmannians

    hep-th 2025-02 conditional novelty 6.0 of 10

    A GLSM defect construction for Schubert cycles in Lagrangian Grassmannians is proposed and checked, with defect indices equal to Schur Q-functions in quantum cohomology and quantum K theory.

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