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Quantum cohomology of flag varieties. (English) Zbl 0847.14011
The quantum cohomology ring of a Kähler manifold is a deformation of the usual cohomology ring introduced by E. Witten [Commun. Math. Phys. 118, No. 3, 411-449 (1988; Zbl 0674.58047)]. The computation of a quantum cohomology ring is generally a difficult task. Givental’ and Kim proposed a presentation of the quantum cohomology rings in the case of flag varieties. In the paper under review a method for computing these rings is described and the presentation proposed by Givental’ and Kim is established. It is observed that this same method should also apply to more general homogeneous spaces.

MSC:
14F99 (Co)homology theory in algebraic geometry
14M15 Grassmannians, Schubert varieties, flag manifolds
81T10 Model quantum field theories
32Q15 Kähler manifolds
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