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Recent progress on the formal degree conjecture

Algebra and Number Theory Seminar

Recent progress on the formal degree conjecture
Series: Algebra and Number Theory Seminar
Location: Zoom Meeting
Presenter: David Schwein, Univ. of Cambridge

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.