AHAHA: Preliminary results on p-adic groups and their representations

Let k be a locally compact non-discrete field with non-Archimedean valuation (Say, just the p-adic numbers Qp), O its ring of integers (say Zp) and P a generator for the maximal ideal of O (i.e. p). In future lectures we will see how Hecke algebras relate to the representation theory of reductive algebraic groups over these fields. The main example to keep in mind is G = GL(n, k). When I talk about open compact subgroups you should think of GL(n,O) and subgroups thereof. Other important subgroups to keep in mind are parabolic subgroups and unipotent subgroups. This will be a basic introduction to the theory of these groups and their representation theory, in particular I will focus on aspects of the theory that are different from say finite groups or Lie groups. Things will be stated in some generality, but I will try to say what the cases we actually care about are.