Quantum Product and Parabolic Orbits in Homogeneous Spaces

Pech, Clelia (2014) Quantum Product and Parabolic Orbits in Homogeneous Spaces. Quantum Product and Parabolic Orbits in Homogeneous Spaces, 42 (11). pp. 4679-4695. ISSN 0092-7872. E-ISSN 1532-4125. (doi:https://doi.org/10.1080/00927872.2013.820736) (Full text available)

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http://www.dx.doi.org/10.1080/00927872.2013.820736

Abstract

Chaput, Manivel, and Perrin proved in [3] 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 relate 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. For all classical Grassmannians, we give a complete description of parabolic orbits associated to cominuscule weights, and we make the decomposition of the Hasse diagram explicit.

Item Type: Article
Additional information: This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra in May 2014, available online: http://wwww.tandfonline.com/10.1080/00927872.2013.820736
Uncontrolled keywords: Generalized flag varieties; Hasse diagrams; Parabolic orbits; Quantum product.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic Geometry
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Clelia Pech
Date Deposited: 20 Oct 2015 10:25 UTC
Last Modified: 27 Jun 2017 11:59 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51096 (The current URI for this page, for reference purposes)
Pech, Clelia: https://orcid.org/0000-0001-6142-6679
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