A Giambelli formula for classical $G/P$ spaces
نویسندگان
چکیده
منابع مشابه
A Giambelli Formula for Classical G/p Spaces
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 H(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 o...
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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 an arbitrary Schubert class in the classical and quantum cohomology ring of X as a polynomial in certain special Schubert classes. Our analysis reveals a surprising relation between the Schubert calcu...
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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 fixed vector space. In the mid 1990s, Fulton, Pragacz, and Ratajski [F3, PR2, FP] asked for global formulas which express the cohomology classes of the universal Schubert varieties in flag bundles – when the space ...
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LetX 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 introduce and study theta polynomials, a family of polynomials which are positive linear combination...
متن کاملA Giambelli Formula for Isotropic Partial Flag Varieties
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 nonrecursive Giambelli formula which expresses an arbitrary Schubert class in H(G/P ) as a polynomial in certain special Schubert class generators; in the even orthogonal case this depends on the main result of [BKT4]. Our formula extends to one that applie...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2013
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-2013-00604-9