On equivariant quantum Schubert calculus for G/P
نویسندگان
چکیده
منابع مشابه
Equivariant Quantum Schubert Calculus
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.
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.
متن کاملEquivariant Schubert Calculus
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 کاملPositivity 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 کاملEquivariant Quantum Schubert Polynomials
We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum cohomology ring, as well as Graham-positivity of the structure constants in equivariant quantum Schubert calculus.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2015
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.05.031