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

Details Gromov-Witten invariants of flag manifolds, via D-modules Gromov-Witten invariants of flag manifolds, via D-modules

2003-06-26

arxiv.org/abs/math/0306372v2

Mathematics

Differential Geometry

19 pages, AMS-TeX. Revised version with some clarifications and corrections

Scientific paper

The quantum cohomology algebra of the (full) flag manifold is a fundamental example in quantum cohomology theory, with connections to combinatorics, algebraic geometry, and integrable systems. Using a differential geometric approach, we give an algorithm for computing the multiplicative structure constants of this algebra (the 3-point genus zero Gromov-Witten invariants). The algorithm involves a Grobner basis calculation and the solution by quadrature of a system of differential equations. In particular we obtain quantum Schubert polynomials in a natural fashion.

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