On the local Langlands correspondence for SL_n Seminar

This will be an introductory talk on the local Langlands correspondence for the special linear group SL_n(F) where F is a local field.

This correspondence parametrises the irreducible smooth representations of SL_n via pairs of parameters.

The first parameter maps into the Langlands dual group, which for SL_n is the complex reductive group PGL_n(C).

The second parameter is an irreducible representation of a certain finite group.

By modifying the finite group, the irreducible smooth representations of SL_n and all of its inner forms can simultaneously be parametrised.

Joint work with Anne-Marie Aubert, Paul Baum, Maarten Solleveld, arXiv:1305.2638 [math.RT], building on work by Hiraga-Saito.