Quantum product and parabolic orbits in homogeneous spaces

Details Quantum product and parabolic orbits in homogeneous spaces Quantum product and parabolic orbits in homogeneous spaces

2012-04-23

arxiv.org/abs/1204.4992v1

Mathematics

Algebraic Geometry

19 pages, 3 figures

Scientific paper

Chaput, Manivel and Perrin proved a formula describing the quantum product by Schubert classes associated to cominuscule weights in a rational projective homogeneous space X. In the case where X has Picard rank one, we link this formula to the stratification of X by P-orbits, where P is the parabolic subgroup associated to the cominuscule weight. We deduce a decomposition of the Hasse diagram of X, i.e the diagram describing the cup-product with the hyperplane class.

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