Geodesic
On Annihilators of Bounded (g, k)-Modules
Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1137-1147
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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.
, M2 are simple (g, k)-modules such that M1 is bounded and the associated varieties of the annihilators of M1 and M2 coincide then M2 is also bounded. This statement is a geometric analogue of a purely algebraic fact due to I. Penkov and V. Serganova, and it was posed as a conjecture in my Ph. D. thesis.
Classification : 13A50, 14L24, 17B08, 17B63, 22E47
Mots-clés : (g, k)-modules, spherical varieties, symplectic geometry 
@article{JLT_2018_28_4_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a10/}
}
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A. 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/JLT_2018_28_4_JLT_2018_28_4_a10/