Geodesic
Gromov-Witten invariants on Grassmannians
Buch, Anders 1   ; Kresch, Andrew 2   ; Tamvakis, Harry 3
1 Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark
2 Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
3 Department of Mathematics, Brandeis University - MS 050, P. O. Box 9110, Waltham, Massachusetts 02454-9110
Journal of the American Mathematical Society, Tome 16 (2003) no. 4, pp. 901-915 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S0894-0347-03-00429-6

Buch, Anders  1   ; Kresch, Andrew  2   ; Tamvakis, Harry  3

1 Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Århus C, Denmark
2 Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
3 Department of Mathematics, Brandeis University - MS 050, P. O. Box 9110, Waltham, Massachusetts 02454-9110 
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Buch, Anders; Kresch, Andrew; Tamvakis, Harry. Gromov-Witten invariants on Grassmannians. Journal of the American Mathematical Society, Tome 16 (2003) no. 4, pp. 901-915. doi: 10.1090/S0894-0347-03-00429-6

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