Geodesic
Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras
Atsumu Sasaki1
1Dept. of Mathematics, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan
Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 597-649

Voir la notice de l'article provenant de la source Heldermann Verlag

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).
Classification : 22E46, 32M10, 32M05, 14M17
Mots-clés : Visible action, multiplicity-free representation, nilpotent orbit, induction theorem

Atsumu Sasaki  1

1 Dept. of Mathematics, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan 
Atsumu Sasaki. Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras. Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 597-649. http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a0/
@article{JOLT_2016_26_3_a0,
     author = {Atsumu Sasaki},
     title = {Visible {Actions} on {Spherical} {Nilpotent} {Orbits} in {Complex} {Simple} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {597--649},
     year = {2016},
     volume = {26},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_3_a0/}
}
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