Gromov-Witten Invariants of Flag Manifolds, VIA D-Modules |
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Authors: | Amarzaya A; Guest M A |
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Institution: | Department of Mathematics, Graduate School of Science, Tokyo Metropolitan University Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan |
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Abstract: | We present a method for computing the 3-point genus zero GromovWitteninvariants of the complex flag manifold G/B from the relationsof the small quantum cohomology algebra QH*G/B (G is a complexsemisimple Lie group and B is a Borel subgroup). In 3] and9], at least in the case G = GLnC, two algebraic/combinatoricmethods have been proposed, based on suitably designed axioms.Our method is quite different, being differential geometricin nature; it is based on the approach to quantum cohomologydescribed in 7], which is in turn based on the integrable systemspoint of view of Dubrovin and Givental. |
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