Algebra Seminar

In the usual theory of smooth representations of an algebraic group G over Q_p one studies irreducible representations which arise in the space of locally constant functions on G.

One can instead consider representations which arise in the space of locally analytic functions on G. I will explain joint work with Matthias Strauch where we construct families of such representations for GL_2, which in a certain sense, p-adically interpolate smooth supercuspidal representations of GL_2. This builds on previous work of Schneider and Teitelbaum who did the analogous thing for principle series.

These locally analytic representations are expected to be the p-adic local factors in certain global objects which are obtained by p-adically interpolating modular forms.