Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 397–415

Polytopes, quasi-minuscule representations and rational surfaces

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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.

Keywords

rational surface minuscule representation polytope 

MSC 2010

14J26 14N20 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsEwha Womans UniversitySeoulKorea
  2. 2.Department of MathematicsSouthwest Jiaotong UniversityChengdu, SichuanP.R. China
  3. 3.Department of MathematicsSichuan UniversityChengdu, SichuanP.R. China

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