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Let X be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses a...
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...
Let G be a classical complex Lie group, P any parabolic subgroup of G, and X = G/P the corresponding homogeneous space, which parametrizes (isotropic) partial flags of subspaces of a fix...
We use Young’s raising operators to introduce and study double theta polynomials, which specialize to both the theta polynomials of Buch, Kresch, and Tamvakis, and to double (or factorial) Schur S-p...
We use Young’s raising operators to introduce and study double eta polynomials, which are an even orthogonal analogue of Wilson’s double theta polynomials. Our double eta polynomials give Giambelli ...
We give a direct proof of the equivalence between the Giambelli and Pieri type formulas for Hall-Littlewood functions using Young’s raising operators, parallel to joint work with Buch and Kresch for ...
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 ...
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 a...
The main result of this note is a Giambelli formula for the Peterson Schubert classes in the S1-equivariant cohomology ring of a type A Peterson variety. Our results depend on the Monk formula for the...

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