منابع مشابه
Quantum Giambelli Formulas for Isotropic Grassmannians
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 authors’ cohomological Giambelli formulas. 0. I...
متن کاملKoppelman Formulas and Existence Theorems for the ∂̄-equation on Analytic Varieties
Let Z be an analytic subvariety of pure codimension p of a pseudoconvex set X in C. We introduce weighted Koppelman formulas on Z that provides solutions to the ∂̄-equation. If φ is a smooth (0, q + 1)-form on Z with ∂̄φ = 0, we find a smooth (0, q)-form ψ on Zreg with at most polynomial growth at Zsing such that ∂̄ψ = φ. We also present Hartogs theorems for ∂̄-closed forms on Z. As a consequence w...
متن کاملPieri-type Formulas for Maximal Isotropic Grassmannians via Triple Intersections
We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The decisive step is an exact description of the intersection of two Schubert varieties, from which the multiplicities (which are powers o...
متن کاملPerverse Sheaves on Grassmannians
We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.
متن کاملRoot games on Grassmannians
We recall the root game, introduced in [P], which gives a fairly powerful sufficient condition for non-vanishing of Schubert calculus on a generalised flag manifold G/B. We show that it gives a necessary and sufficient rule for nonvanishing of Schubert calculus on Grassmannians. In particular, a LittlewoodRichardson number is non-zero if and only if it is possible to win the corresponding root ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2010
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2010.021