Quantum cohomology of minuscule homogeneous spaces III : semi-simplicity and consequences

Details Quantum cohomology of minuscule homogeneous spaces III : semi-simplicity and consequences Quantum cohomology of minuscule homogeneous spaces III : semi-simplicity and consequences

2007-10-05

arxiv.org/abs/0710.1224v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, specialized at q=1, is semisimple. This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized at the quantum parameter. We check that this involution coincides with the strange duality defined in a previous paper. We deduce Vafa-Intriligator type formulas for the Gromov-Witten invariants.

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