We construct a family of exact functors from the BGG category O of representations of the Lie algebra sln(C) to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained.

We consider graded finitely presented algebras and modules over a field. Under some restrictions, the set of Hilbert series of such algebras (or modules) becomes finite. Claims of that types imply rationality of Hilbert and Poincare series of some algebras and modules, including periodicity of Hilbert functions of common (e.g., Noetherian) modules and algebras of linear growth.