A Giambelli formula for classical $G/P$ spaces

Abstract

Let $G$ be a classical complex Lie group, $P$ any parabolic subgroup of $G$, and $G/P$ the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in the cohomology ring of $G/P$ as a polynomial in certain special Schubert class generators. Our formula extends to one that applies to the torus-equivariant cohomology ring of $G/P$ and to the setting of symplectic and orthogonal degeneracy loci.

26 pages; new title. This final version corrects two minor errors, on pages 10 and 22, which appear in the journal reference

References in corpus (6)

• Quantum Pieri rules for isotropic Grassmannians
• Double Schubert polynomials for the classical groups
• A Giambelli formula for isotropic Grassmannians
• Schubert polynomials and Arakelov theory of symplectic flag varieties
• Quantum Giambelli formulas for isotropic Grassmannians
• Schubert polynomials and Arakelov theory of orthogonal flag varieties

Cited by in corpus (1)

• A Giambelli formula for isotropic Grassmannians