Recent progress on the formal degree conjecture

Abstract: The local Langlands correspondence is more than a correspondence: it promises an extensive dictionary between the representation theory of reductive p-adic groups and the arithmetic of their L-parameters. One entry in this dictionary is a conjectural formula of Hiraga, Ichino, and Ikeda for the size of a discrete series representation – its “formal degree” – in terms of a gamma factor of its L-parameter. In the first part of the talk, I’ll explain why the conjecture is true for almost all supercuspidal representations. In the second part, I’ll compute the sign of the gamma factor, verifying a conjecture of Gross and Reeder.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar