A twisted Yu construction and Harish-Chandra characters

Abstract: In 2001 J.K.Yu gave a general construction of supercuspidal representations of reductive $p$-adic groups. It was shown by Kim and Fintzen that all supercuspidal representations arise from it when $p$ is not too small. I will discuss a twist of this construction, which resolves a recently discovered error in Yu's paper. I will then discuss the following applications that this twisted construction makes possible: (i) a formula for the Harish-Chandra character of the resulting representations without compactness or shallowness assumptions, (ii) a construction of the local Langlands correspondence for arbitrary supercuspidal parameters when $p$ is not too small, (iii) the proof of endoscopic transfer for regular supercuspidal L-packets. This is joint work, partly in progress, with Fintzen and Spice.

number theoryrepresentation theory

Audience: researchers in the topic

Cross Atlantic Representation Theory and Other topics ONline (CARTOON) conference