Type: Article
Publication Date: 2003-05-01
Citations: 123
DOI: https://doi.org/10.1090/s0894-0347-03-00429-6
We prove that any three-point genus zero Gromov-Witten invariant on a type $A$ Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step flag variety is replaced by a sub-maximal isotropic Grassmannian. Our theorems are applied, in type $A$, to formulate a conjectural quantum Littlewood-Richardson rule, and in the other classical Lie types, to obtain new proofs of the main structure theorems for the quantum cohomology of Lagrangian and orthogonal Grassmannians.