Last updated: April 12, 2005
Let G be a connected reductive complex group, with a fixed involution θ; let K be the group of θ-fixed points in G, and g=Lie(G).
The second major goal of the program, barely begun at this time, is to give access to the "local" aspects of the theory of (g,K)-modules for G (by this, we mean questions that only involve representations at a fixed infinitesimal character, say.) More precisely, we will deal with the following questions:
Eventually, we plan to treat these questions in full generality, i.e., for arbitrary infinitesimal characters, possibly singular or non-integral. For the near future, however, we will concentrate on the case of regular integral infinitesimal character.