## Gromov-Witten invariants on Grassmannians

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- by Anders Skovsted Buch, Andrew Kresch and Harry Tamvakis;
- J. Amer. Math. Soc.
**16**(2003), 901-915 - DOI: https://doi.org/10.1090/S0894-0347-03-00429-6
- Published electronically: May 1, 2003
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## 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.## References

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## Bibliographic Information

**Anders Skovsted Buch**- Affiliation: Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark
- MR Author ID: 607314
- Email: abuch@imf.au.dk
**Andrew Kresch**- Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
- MR Author ID: 644754
- Email: kresch@math.upenn.edu
**Harry Tamvakis**- Affiliation: Department of Mathematics, Brandeis University - MS 050, P. O. Box 9110, Waltham, Massachusetts 02454-9110
- Email: harryt@brandeis.edu
- Received by editor(s): July 18, 2002
- Published electronically: May 1, 2003
- Additional Notes: The authors were supported in part by NSF Grant DMS-0070479 (Buch), an NSF Postdoctoral Research Fellowship (Kresch), and NSF Grant DMS-0296023 (Tamvakis).
- © Copyright 2003 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**16**(2003), 901-915 - MSC (2000): Primary 14N35; Secondary 14M15, 14N15, 05E15
- DOI: https://doi.org/10.1090/S0894-0347-03-00429-6
- MathSciNet review: 1992829