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.
| Original language | English |
|---|---|
| Pages (from-to) | 397-415 |
| Number of pages | 19 |
| Journal | Czechoslovak Mathematical Journal |
| Volume | 67 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Jun 2017 |
Bibliographical note
Publisher Copyright:© 2017, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.
Keywords
- minuscule representation
- polytope
- rational surface