BOUNDED REDUCTIVE SUBALGEBRAS OF sl(n)

作者：Petukhov Alexey V^*

来源：Transformation Groups, 2011, 16(4): 1173-1182.

DOI：10.1007/s00031-011-9152-7

Let g be a reductive Lie algebra and t subset of g be a reductive in g subalgebra. A (g; t)-module M is a g -module for which any element m is an element of M is contained in a fi nite-dimensional t -submodule of M. We say that a (g, t)-module M is bounded if there exists a constant C-M such that the Jordan-Holder multiplicities of any simple finite-dimensional t -module in every fi nite-dimensional t -submodule of M are bounded by C-M. In the present paper we describe explicitly all reductive in sl(n) subalgebras t which admit a bounded simple in fi nite-dimensional (sl(n); t)-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 (g; t)-modules.

• 出版日期2011-12