On Annihilators of Bounded (g, k)-Modules

A. Petukhov

doi:10.5802/jolt.1042

A. Petukhov

Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1137-1147

Abstract

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

Zbl

DOI: 10.5802/jolt.1042

Classification: 13A50, 14L24, 17B08, 17B63, 22E47
Keywords: (g, k)-modules, spherical varieties, symplectic geometry

@article{JOLT_2018_28_4_a10,
     author = {A. Petukhov},
     title = {On {Annihilators} of {Bounded} (g, {k)-Modules}},
     journal = {Journal of Lie Theory},
     pages = {1137--1147},
     year = {2018},
     volume = {28},
     number = {4},
     doi = {10.5802/jolt.1042},
     zbl = {1441.17007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1042/}
}

TY  - JOUR
AU  - A. Petukhov
TI  - On Annihilators of Bounded (g, k)-Modules
JO  - Journal of Lie Theory
PY  - 2018
SP  - 1137
EP  - 1147
VL  - 28
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1042/
DO  - 10.5802/jolt.1042
ID  - JOLT_2018_28_4_a10
ER  -

%0 Journal Article
%A A. Petukhov
%T On Annihilators of Bounded (g, k)-Modules
%J Journal of Lie Theory
%D 2018
%P 1137-1147
%V 28
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1042/
%R 10.5802/jolt.1042
%F JOLT_2018_28_4_a10

A. Petukhov. On Annihilators of Bounded (g, k)-Modules. Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1137-1147. doi: 10.5802/jolt.1042

Cited by Sources: