Mathematical Research Letters

Volume 28 (2021)

Number 4

On the formal degree conjecture for simple supercuspidal representations

Pages: 1227 – 1242

DOI:  https://dx.doi.org/10.4310/MRL.2021.v28.n4.a11

Author

Yoichi Mieda (Graduate School of Mathematical Sciences, University of Tokyo, Japan)

Abstract

We prove the formal degree conjecture for simple supercuspidal representations of symplectic groups and quasi-split even special orthogonal groups over a $p$‑adic field, under the assumption that $p$ is odd. The essential part is to compute the Swan conductor of the exterior square of an irreducible local Galois representation with Swan conductor $1$. It is carried out by passing to an equal characteristic local field and using the theory of Kloosterman sheaves.

Received 29 August 2019

Accepted 23 June 2020

Published 22 November 2021