On Annihilators of Bounded (g, k)-Modules
Journal of Lie Theory, Tome 28 (2018) no. 4, pp. 1137-1147
Voir la notice de l'article provenant de la source Heldermann Verlag
Let g be a semisimple Lie algebra and k a reductive subalgebra. We say that a g-module M is a bounded (g, k)-module if M is a direct sum of simple finite-dimensional k-modules and the multiplicities of all simple k-modules in this direct sum are universally bounded.
The goal of this article is to show that the "boundedness" property for a simple (g, k)-module M is equivalent to a property of the associated variety of the annihilator of M (this is the closure of a nilpotent coadjoint orbit inside g* under the assumption that the main field is algebraically closed and of characteristic 0. In particular this implies that if M
The goal of this article is to show that the "boundedness" property for a simple (g, k)-module M is equivalent to a property of the associated variety of the annihilator of M (this is the closure of a nilpotent coadjoint orbit inside g* under the assumption that the main field is algebraically closed and of characteristic 0. In particular this implies that if M
Classification :
13A50, 14L24, 17B08, 17B63, 22E47
Mots-clés : (g, k)-modules, spherical varieties, symplectic geometry
Mots-clés : (g, k)-modules, spherical varieties, symplectic geometry
Affiliations des auteurs :
Alexey Petukhov 1
Alexey Petukhov. On Annihilators of Bounded (g, k)-Modules. Journal of Lie Theory, Tome 28 (2018) no. 4, pp. 1137-1147. http://geodesic.mathdoc.fr/item/JOLT_2018_28_4_a10/
@article{JOLT_2018_28_4_a10,
author = {Alexey Petukhov},
title = {On {Annihilators} of {Bounded} (g, {k)-Modules}},
journal = {Journal of Lie Theory},
pages = {1137--1147},
year = {2018},
volume = {28},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2018_28_4_a10/}
}