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 the equal characteristic local field and using the theory of Kloosterman sheaves.
Endoscopic lifting of simple supercuspidal representations of SO(2n+1) to GL(2n)
Endoscopic lifting of simple supercuspidal representations of U(N) to GL(N)
Simple supercuspidal representations of $\mathrm{GSp}_4$ and test vectors
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