Abstract for Lecture 3:

Continuous representations of p-adic groups constructed by geometry almost never are Banach space representations but rather Frechet spaces. This leads to the concept of a locally analytic representation. Although much more complicated as a topological vector space it has the advantage that it allows a derived action of the Lie algebra. Again I will construct a suitable abelian category of locally analytic representations. It contains the classical category of admissible smooth representations (in the sense of Harish Chandra) as a full subcategory.