Canonical domains for coadjoint orbits of compact Lie algebras (David Martinez Torres, Rio-de-Janeiro)

30.01.2020 14:00 – 16:00

The purpose of this talk is to describe for any coadjoint orbit of a compact Lie algebra a symplectomorphism from an open dense subset to a (starshaped) domain of a cotangent bundle. In other words, we show that any such coadjoint orbit is symplectically the compactification of a domain of a cotangent bundle.
The tools include Lie theory of semisimple Lie algebras and Lie groups, a geometric description of Kahler potentials introduced by Donaldson and an old characterization of cotangent bundles described by Nagano.
If time permits, we will discuss a second type of symplectomorphisms which establish a symplectic duality of sorts between coadjoint orbits of compact Lie algebras and hyperbolic orbits of non-compact semisimple Lie algebras.

Lieu

Bâtiment: Battelle

Villa Battelle, Séminaire "Groupes de Lie et espaces des modules"

entrée libre