Seminar

Let K be a finite extension of Qp. It is known for some time that one cannot expect a bijection between smooth irreducible admissible representations of GLn(K) and smooth n-dimensional representations of Gal(Kbar/K), both over Fpbar. However, one can still hope for a ``good understanding'' of the representations of GLn(K) occuring as Hecke Eigenspaces of mod p automorphic forms (for, say, compact unitary groups).

When K is unramified, I will present some conjectures on the generic structure of these GLn(K)-representations, and the way this structure is related to the underlying Gal(Kbar/K)-representation. Then I will give some fragmentary evidence (due to many people) which support these conjectures.

This is joint work (in progress) with Florian Herzig and Benjamin Schraen.