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Journal of the London Mathematical Society 2005 72(1):121-136; doi:10.1112/S0024610705006381
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© The London Mathematical Society

Gromov–Witten Invariants of Flag Manifolds, VIA D-Modules

A. Amarzaya and M. A. Guest

Department of Mathematics, Graduate School of Science, Tokyo Metropolitan University Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan

Received 27 March 2003. Revision received 26 August 2004.

We present a method for computing the 3-point genus zero Gromov–Witten invariants of the complex flag manifold G/B from the relations of the small quantum cohomology algebra QH*G/B (G is a complex semisimple Lie group and B is a Borel subgroup). In [3] and [9], at least in the case G = GLnC, 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.

School of Mathematics and Computer Science, National University of Mongolia, Ulannbaatar, Post Box 586, Post Office 46-A, Mongolia


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