Polytopes,quasi-minuscule representations and rational surfaces |
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Authors: | Jae-Hyouk Lee Mang Xu Jiajin Zhang |
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Affiliation: | 1.Department of Mathematics,Ewha Womans University,Seoul,Korea;2.Department of Mathematics,Southwest Jiaotong University,Chengdu, Sichuan,P.R. China;3.Department of Mathematics,Sichuan University,Chengdu, Sichuan,P.R. China |
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Abstract: | 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. |
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