Polytopes, quasi-minuscule representations and rational surfaces

Jae-Hyouk Lee; Mang Xu; Jiajin Zhang

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 2, page 397-415
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Lee, Jae-Hyouk, Xu, Mang, and Zhang, Jiajin. "Polytopes, quasi-minuscule representations and rational surfaces." Czechoslovak Mathematical Journal 67.2 (2017): 397-415. <http://eudml.org/doc/288198>.

@article{Lee2017,
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.},
author = {Lee, Jae-Hyouk, Xu, Mang, Zhang, Jiajin},
journal = {Czechoslovak Mathematical Journal},
keywords = {rational surface; minuscule representation; polytope},
language = {eng},
number = {2},
pages = {397-415},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Polytopes, quasi-minuscule representations and rational surfaces},
url = {http://eudml.org/doc/288198},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Lee, Jae-Hyouk
AU - Xu, Mang
AU - Zhang, Jiajin
TI - Polytopes, quasi-minuscule representations and rational surfaces
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 397
EP - 415
AB - 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.
LA - eng
KW - rational surface; minuscule representation; polytope
UR - http://eudml.org/doc/288198
ER -

References

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