
Journal of Lie Theory 28 (2018), No. 4, 11371147 Copyright Heldermann Verlag 2018 On Annihilators of Bounded (g, k)Modules Alexey Petukhov Institute for Information Transmission Problems, Bolshoy Karetniy 191, Moscow, 127994, Russia alex2@yandex.ru Let g be a semisimple Lie algebra and k a reductive subalgebra. We say that a gmodule M is a bounded (g, k)module if M is a direct sum of simple finitedimensional kmodules and the multiplicities of all simple kmodules 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 Keywords: (g, k)modules, spherical varieties, symplectic geometry. MSC: 13A50, 14L24, 17B08, 17B63, 22E47. [ Fulltextpdf (116 KB)] for subscribers only. 