# A Giambelli formula for isotropic Grassmannians

Buch, Anders Skovsted; Kresch, Andrew; Tamvakis, Harry (2017). A Giambelli formula for isotropic Grassmannians. Selecta Mathematica, 23(2):869-914.

## Abstract

Let $X$ be a symplectic or odd orthogonal Grassmannian. We prove a Giambelli formula which expresses an arbitrary Schubert class in $H^{∗}(X,Z)$ as a polynomial in certain special Schubert classes. This polynomial, which we call a theta polynomial, is defined using raising operators, and we study its image in the ring of Billey–Haiman Schubert polynomials.

## Abstract

Let $X$ be a symplectic or odd orthogonal Grassmannian. We prove a Giambelli formula which expresses an arbitrary Schubert class in $H^{∗}(X,Z)$ as a polynomial in certain special Schubert classes. This polynomial, which we call a theta polynomial, is defined using raising operators, and we study its image in the ring of Billey–Haiman Schubert polynomials.

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