Original scientific paper

https://doi.org/10.3336/gm.56.2.06

Approximation of nilpotent orbits for simple Lie groups

Lucas Fresse ; Institut Elie Cartan de Lorraine, CNRS - UMR 7502, Université de Lorraine, France
Salah Mehdi ; Institut Elie Cartan de Lorraine, CNRS - UMR 7502, Université de Lorraine, France

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Abstract

We propose a systematic and topological study of limits
\(\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)\) of continuous families
of adjoint orbits for a non-compact simple real Lie group
\(G_\mathbb{R}\). 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
\(\mathrm{SL}_n(\mathbb{R})\) and \(\mathrm{SU}(p,q)\) are computed in
detail.

Keywords

Lie groups, semisimple and nilpotent orbits, approximation, asymptotic cones

Hrčak ID:

267558

URI

https://hrcak.srce.hr/267558

Publication date:

23.12.2021.

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