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arXiv · 1204.4992

Quantum product and parabolic orbits in homogeneous spaces

Clélia Pech
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Abstract

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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Clélia Pech. 2012-04-23. Quantum product and parabolic orbits in homogeneous spaces. https://arxiv.org/abs/1204.4992

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