caa a22 4500 445862548 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00031-011-9152-7 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9152-7 Petukhov Alexey Chair of High Algebra, Department of Mechanics and Mathematics, Moscow State University, GSP-2, 119992, Moscow, Russia aut Bounded reductive subalgebras of $ \mathfrak{s}{\mathfrak{l}_n} $ [Elektronische Daten] [Alexey Petukhov] Let $ \mathfrak{g} $ be a reductive Lie algebra and $ \mathfrak{k} \subset \mathfrak{g} $ be a reductive in $ \mathfrak{g} $ subalgebra. A ( $ \mathfrak{g},\mathfrak{k} $ )-module M is a $ \mathfrak{g} $ -module for which any element m ∈ M is contained in a finite-dimensional $ \mathfrak{k} $ -submodule of M. We say that a ( $ \mathfrak{g},\mathfrak{k} $ )-module M is bounded if there exists a constant C M such that the Jordan-Hölder multiplicities of any simple finite-dimensional $ \mathfrak{k} $ -module in every finite-dimensional $ \mathfrak{k} $ -submodule of M are bounded by C M . In the present paper we describe explicitly all reductive in $ \mathfrak{s}{\mathfrak{l}_n} $ subalgebras $ \mathfrak{k} $ which admit a bounded simple infinite-dimensional ( $ \mathfrak{s}{\mathfrak{l}_n},\mathfrak{k} $ )-module. Our technique is based on symplectic geometry and the notion of spherical variety. We also characterize the irreducible components of the associated varieties of simple bounded ( $ \mathfrak{g},\mathfrak{k} $ )-modules. Springer Science+Business Media, LLC, 2011 Transformation Groups SP Birkhäuser Verlag Boston 16/4(2011-12-01), 1173-1182 1083-4362 16:4<1173 2011 16 31 https://doi.org/10.1007/s00031-011-9152-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9152-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Petukhov Alexey Chair of High Algebra, Department of Mechanics and Mathematics, Moscow State University, GSP-2, 119992, Moscow, Russia aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/4(2011-12-01), 1173-1182 1083-4362 16:4<1173 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer