Polytopes, quasi-minuscule representations and rational surfaces

Jae Hyouk Lee, Mang Xu, Jiajin Zhang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)397-415
Number of pages19
JournalCzechoslovak Mathematical Journal
Issue number2
StatePublished - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2017, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.


  • minuscule representation
  • polytope
  • rational surface


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