Gromov-Witten invariants on Grassmannians

Details Gromov-Witten invariants on Grassmannians Gromov-Witten invariants on Grassmannians

2003-06-27

arxiv.org/abs/math/0306388v1

Mathematics

Algebraic Geometry

15 pages, LaTeX2e, to appear in J. Amer. Math. Soc

Scientific paper

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.

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