Approximation of nilpotent orbits for simple lie groups

Lucas Fresse (1) , Salah Mehdi (1)

1 IECL - Institut Élie Cartan de Lorraine

We propose a systematic and topological study of limits lim ν→0 + G R ⋅(νx) of continuous families of adjoint orbits for a non-compact simple real Lie group G R. This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of SLn(R) and SU(p, q) are computed in detail.

Mots clés: Lie groups; semisimple and nilpotent orbits; approximation; asymptotic cones

Domaines: Mathématiques [math]

Lucas Fresse, Salah Mehdi. Approximation of nilpotent orbits for simple lie groups. Glasnik Matematicki, inPress. ⟨hal-03336270⟩