On the formal degree conjecture for non-singular supercuspidal representations

We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein’s work [Sch21] proving the formal degree conjecture for regular supercuspidal representations. The main difference between our work and Schwein’s work is that in nonsingular case, the Deligne–Lusztig representations can be reducible, and the S-groups are not necessary abelian. Therefore, we have to compare the dimensions of irreducible constituents of the Deligne–Lusztig representations and the dimensions of irreducible representations of Sgroups.