Polytopes, quasi-minuscule representations and rational surfaces

Lee, Jae-Hyouk ; Xu, Mang ; Zhang, Jiajin

Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 397-415

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2017.0676-15

Classification : 14J26, 14N20
Keywords: rational surface; minuscule representation; polytope

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