Visible actions on spherical nilpotent orbits in complex simple Lie algebras
Representation Theory
2017-12-20 v1
Abstract
This paper studies nilpotent orbits in complex simple Lie algebras from the viewpoint of strongly visible actions in the sense of T. Kobayashi. We prove that the action of a maximal compact group consisting of inner automorphisms on a nilpotent orbit is strongly visible if and only if it is spherical, namely, admitting an open orbit of a Borel subgroup. Further, we find a concrete description of a slice in the strongly visible action. As a corollary, we clarify a relationship among different notions of complex nilpotent orbits: actions of Borel subgroups (sphericity); multiplicity-free representations in regular functions; momentum maps; and actions of compact subgroups (strongly visible actions).
Cite
@article{arxiv.1509.07281,
title = {Visible actions on spherical nilpotent orbits in complex simple Lie algebras},
author = {Atsumu Sasaki},
journal= {arXiv preprint arXiv:1509.07281},
year = {2017}
}