## Osaka Journal of Mathematics

#### Abstract

We study coadjoint orbitopes, i.e. convex hulls of coadjoint orbits of compact Lie groups. We show that up to conjugation the faces are completely determined by the geometry of the faces of the convex hull of Weyl group orbits. We also consider the geometry of the faces and show that they are themselves coadjoint orbitopes. From the complex geometric point of view the sets of extreme points of a face are realized as compact orbits of parabolic subgroups of the complexified group.

#### Article information

Source
Osaka J. Math., Volume 51, Number 4 (2014), 935-969.

Dates
First available in Project Euclid: 31 October 2014

https://projecteuclid.org/euclid.ojm/1414761906

Mathematical Reviews number (MathSciNet)
MR3273872

Zentralblatt MATH identifier
1305.22011

Subjects
Primary: 22E46: Semisimple Lie groups and their representations 53D26

#### Citation

Biliotti, Leonardo; Ghigi, Alessandro; Heinzner, Peter. Coadjoint orbitopes. Osaka J. Math. 51 (2014), no. 4, 935--969. https://projecteuclid.org/euclid.ojm/1414761906

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