Resumen de Gromov-Witten invariants of flag manifolds, via D-modules

A. Amarzaya, M. A. Guest

• We present a method for computing the 3-point genus zero Gromov-Witten invariants of the complex flag manifold from the relations of the small quantum cohomology algebra ( is a complex semisimple Lie group and is a Borel subgroup). In [3] and [9], at least in the case , two algebraic/combinatoric methods have been proposed, based on suitably designed axioms. Our method is quite different, being differential geometric in nature; it is based on the approach to quantum cohomology described in [7], which is in turn based on the integrable systems point of view of Dubrovin and Givental.