Journal of Lie Theory

no. 3
Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras
Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 597-649
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).
DOI: 10.5802/jolt.902
Classification: 22E46, 32M10, 32M05, 14M17
Keywords: Visible action, multiplicity-free representation, nilpotent orbit, induction theorem 
@article{JOLT_2016_26_3_a0,
     author = {A. 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},
     doi = {10.5802/jolt.902},
     zbl = {1406.17012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.902/}
}
TY  - JOUR
AU  - A. Sasaki
TI  - Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras
JO  - Journal of Lie Theory
PY  - 2016
SP  - 597
EP  - 649
VL  - 26
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.902/
DO  - 10.5802/jolt.902
ID  - JOLT_2016_26_3_a0
ER  - 
%0 Journal Article
%A A. Sasaki
%T Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras
%J Journal of Lie Theory
%D 2016
%P 597-649
%V 26
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.902/
%R 10.5802/jolt.902
%F JOLT_2016_26_3_a0
A. Sasaki. Visible Actions on Spherical Nilpotent Orbits in Complex Simple Lie Algebras. Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 597-649. doi: 10.5802/jolt.902

Cited by Sources: