### School of Mathematics and Statistics

### Mark Kisin

University of Munster

### Locally analytic representations for GL_2(Q_p).

**Friday 11th January, 12-1pm,
Carslaw 375. **

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.