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Gromov-Witten invariants on Grassmannians


Buch, A; Kresch, A; Tamvakis, H (2003). Gromov-Witten invariants on Grassmannians. Journal of the American Mathematical Society, 16(4):901-915.

Abstract

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.

Abstract

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2003
Deposited On:27 Feb 2010 01:40
Last Modified:02 Jun 2016 18:28
Publisher:American Mathematical Society
ISSN:0894-0347
Additional Information:First published in Journal of the American Mathematical Society in Vol.16 Number 4,2003, published by the American Mathematical Society
Publisher DOI:https://doi.org/10.1090/S0894-0347-03-00429-6

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