Lee, Jae-Hyouk; Xu, Mang; Zhang, Jiajin Polytopes, quasi-minuscule representations and rational surfaces. (English) Zbl 1458.14051 Czech. Math. J. 67, No. 2, 397-415 (2017). Summary: 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. MSC: 14J26 Rational and ruled surfaces 14N20 Configurations and arrangements of linear subspaces 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B20 Simple, semisimple, reductive (super)algebras Keywords:rational surface; minuscule representation; polytope PDFBibTeX XMLCite \textit{J.-H. Lee} et al., Czech. Math. J. 67, No. 2, 397--415 (2017; Zbl 1458.14051) Full Text: DOI