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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
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