Quantum Giambelli formulas for isotropic Grassmannians

TL;DR

This paper establishes quantum Giambelli formulas for isotropic Grassmannians, providing explicit polynomial expressions for Schubert classes in their quantum cohomology rings, extending classical formulas to quantum settings.

Contribution

It extends classical Giambelli formulas to the quantum cohomology of symplectic and orthogonal Grassmannians, providing explicit polynomial expressions for Schubert classes.

Findings

Derived quantum Giambelli formulas for isotropic Grassmannians.

Extended classical cohomological formulas to quantum cohomology.

Provided explicit polynomial expressions for Schubert classes.

Abstract

Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class in the small quantum cohomology ring of X as a polynomial in certain special Schubert classes, extending the cohomological Giambelli formulas of arXiv:0811.2781.