Quantum product and parabolic orbits in homogeneous spaces

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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.
Original languageEnglish
Place of PublicationN/A
Number of pages19
ISBN (Print)N/A
Publication statusE-pub ahead of print - 23 Apr 2012


  • math.AG


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