Abstract:

We will discuss the connections between the homological properties of the representation theory of the general linear group over a p-adic field and the representation theory of the complex semisimple Lie algebra sln(C). We use the Arakawa-Suzuki functors, a family of exact functors from the BGG category O of sln(C) to the category of finite dimensional modules over the degenerate affine Hecke algebra, to extract new homological results in the setting of the general linear group from known results in the theory of the category O.