Positivity in equivariant Schubert calculus
نویسندگان
چکیده
منابع مشابه
Positivity in Equivariant Schubert Calculus
We prove a positivity property for the cup product in the T -equivariant cohomology of the flag variety. This was conjectured by D. Peterson and has as a consequence a conjecture of S. Billey. The result for the flag variety follows from a more general result about algebraic varieties with an action of a solvable linear algebraic group such that the unipotent radical acts with finitely many orb...
متن کاملPositivity in Equivariant Quantum Schubert Calculus
A conjecture of D. Peterson, proved by W. Graham [Gr], states that the structure constants of the (T−)equivariant cohomology of a homogeneous space G/P satisfy a certain positivity property. In this paper we show that this positivity property holds in the more general situation of equivariant quantum cohomology.
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We study the T−equivariant quantum cohomology of the Grassmannian. We prove the vanishing of a certain class of equivariant quantum Littlewood-Richardson coefficients, which implies an equivariant quantum Pieri rule. As in the equivariant case, this implies an algorithm to compute the equivariant quantum Littlewood-Richardson coefficients.
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Let T be a torus acting on C in such a way that, for all 1 ≤ k ≤ n, the induced action on the grassmannian G(k, n) has only isolated fixed points. The T -equivariant cohomology of G(k, n) can be realized, in this case, as the quotient of a ring generated by derivations on the exterior algebra of a free module of rank n over the T -equivariant cohomology of a point. This result allows a simple e...
متن کاملExcited Young Diagrams and Equivariant Schubert Calculus
We describe the torus-equivariant cohomology ring of isotropic Grassmannians by using a localization map to the torus fixed points. We present two types of formulas for equivariant Schubert classes of these homogeneous spaces. The first formula involves combinatorial objects which we call “excited Young diagrams” and the second one is written in terms of factorial Schur Qor P -functions. As an ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2001
ISSN: 0012-7094
DOI: 10.1215/dmj/1000314066