Abstract:
Let G be a p-adic reductive group (e.g. GL_n(Q_p)) and let I be a pro-p Iwahori subgroup of G (e.g. matrices over Z_p which are upper unitriangular modulo p). In the study of so-called smooth G-representations over a field k of characteristic p, one is naturally led to consider the convolution algebra H=k[I\G/I] of I-bilinear compactly supported functions on G and its associated category of modules. These categories (of smooth representations and H-modules) are of great interest in the Langlands program. In earlier work with J.Kohlhaase, we proposed to study a certain localisation Ho(H) of Mod(H), due to Hovey, which arises as the homotopy category of some model structure. It is a triangulated category which is in a suitable sense analogous to the stable module categories appearing in the modular representation theory of finite groups. In this talk, I will present results on the structure of Ho(H), which can be glued from smaller analogous categories via certain recollements, and on the classification of isomorphism classes of simple modules in Ho(H).