Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries

Details Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries

2006-09-28

arxiv.org/abs/math/0609796v1

International Mathematics Research Notices (2007) ID rnm107

Mathematics

Algebraic Geometry

17 pages

Scientific paper

10.1093/imrn/rnm107

We prove that the quantum cohomology ring of any minuscule or cominuscule
homogeneous space, once localized at the quantum parameter, has a non trivial
involution mapping Schubert classes to multiples of Schubert classes. This can
be stated as a strange duality property for the Gromov-Witten invariants, which
turn out to be very symmetric.

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