Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 26 (2016), No. 3, 597--649
Copyright Heldermann Verlag 2016

Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras

Atsumu Sasaki
Dept. of Mathematics, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan

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).

Keywords: Visible action, multiplicity-free representation, nilpotent orbit, induction theorem.

MSC: 22E46; 32M10, 32M05, 14M17

[ Fulltext-pdf  (468  KB)] for subscribers only.