Number Theory Seminar: Geo Kam-Fai Tam

Part I: Representations of reductive groups over local fields

In this talk, we describe the representations of certain reductive groups over local fields and the representations of Weil groups. Then we review the class field theory for local fields and the Langlands correspondence for these reductive groups. The talk will be a brief overview of the representation theory of reductive groups over local fields, largely based on examples of low-rank groups.

Part II: Endoscopic classification of essentially tame supercuspidal representations for quasi-split classical groups

Continue from the last talk, we specify our reductive group \mathbf{G} to be a quasi-split classical group (special orthogonal, symplectic, unitary) over a p-adic field of odd residual characteristic. We describe the endoscopic classification, proved by Arthur and Mok, of certain supercuspidal representations and their L-packets of \mathbf{G}, under some regularity and tameness conditions. These representations can be described by inducing types constructed by Bushnell-Kutzko, Stevens, or Yu, and they correspond to Langlands parameters related to characters of elliptic maximal tori of \mathbf{G}. (This work is partly joint with Corinne Blondel.)