Principal series representations of quasi-split p-adic groups

Abstract:

Kazhdan and Lusztig famously parametrized the Iwahori-spherical representations of split reductive

p-adic groups. That can be considered as one of the first instances of the local Langlands correspondence,

and as a starting point for the role of affine Hecke algebras in the Langlands program.

In this talk we discuss the local Langlands correspondence for all principal series representations

of quasi-split reductive p-adic groups, which was established recently. This is a generalization of the

Iwahori-spherical case which still bears considerable similarity with that case. However, the proof is

in many ways completely different from the work of Kazhdan—Lusztig. For example, in our setting the

affine Hecke algebras do not arise from types, and in these algebras different roots may have different

q-parameters. We will explain some parts of the proof of the correspondence, in particular how

generic representations are used to make it canonical.

Predavanje će se održati preko platforme Zoom. Podaci za priključenje:

Topic: Seminar za unitarne reprezentacije i automorfne forme

Time: May 22, 2023 04:00 PM Europe/Zagreb

Join Zoom Meeting

https://zoom.us/j/93233493717?pwd=YmZubDhWelI5VFhmM0RSc3JzeW5MZz09

Meeting ID: 932 3349 3717

Pozivaju se članovi seminara i svi zainteresirani.
 M.Hanzer