A completely integrable system on $G_2$ coadjoint orbits

Abstract

We construct a Gelfand-Zeitlin system on a one-parameter family of $G_2$ coadjoint orbits that are multiplicity-free Hamiltonian $SU(3)$-spaces. Using this system we prove a lower bound for the Gromov width of these orbits. This lower bound agrees with the known upper bound.

although the concept and results are correct, the work has technical flaws which i do not have time to correct

References in corpus (3)

• Convexity and Thimm's Trick
• The Gromov width of coadjoint orbits of the symplectic group
• On the Gromov width of homogeneous Kaehler manifolds

Cited by in corpus (1)

• Simplices in Newton-Okounkov bodies and the Gromov width of coadjoint orbits