RTG Number Theory: Internal structure of L-packets for p-adic groups

Abstract: The local Langlands correspondence predicts that there is a finite-to-one map between the set of irreducible, admissible representations of a group G and the set of L-parameters of G. While the local Langlands correspondence has been established in many cases, the internal structure of L-packets is not explicitly known except in a few special cases. In this talk, we will describe one approach to study the internal structure. This approach is based on the case of SL(2,Qp) whose L-packets are parametrized by irreducible representations of subgroups of the Klein 4-group.