Supports of (g,k)-moduli of finite type / A. V. Petukhov. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 3. P. 51-55 [Moscow Univ. Math. Bulletin. Vol. 67, N 3, 2012.].
Let g be a semisimple Lie algebra and k be a reductive subalgebra in g. We say that a g-module M is a (g,k)-module if M, considered as a k-module, is a direct sum of finite-dimensional k-modules. We say that a (g,k)-module M is of finite type if all k-isotypic components of M are finite-dimensional. In this article we prove that any simple (g,k)-module of finite type is holonomic. To a simple g-module M one assigns invariants V(M), V(LocM) and L(M) reflecting the "directions of growth of M". We also prove that, for a given pair (g,k), the set of possible invariants is finite.
Key words: (g,k)-module, coadjoint orbit, null-cone.