Geodesic
Polytopes, quasi-minuscule representations and rational surfaces
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 397-415.

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We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural numerical conditions.
DOI : 10.21136/CMJ.2017.0676-15
Classification : 14J26, 14N20
Keywords: rational surface; minuscule representation; polytope 
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Lee, Jae-Hyouk; Xu, Mang; Zhang, Jiajin. Polytopes, quasi-minuscule representations and rational surfaces. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 397-415. doi : 10.21136/CMJ.2017.0676-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0676-15/

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