On the Formal Degree Conjecture for Non-Singular Supercuspidal Representations

Abstract

Abstract We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein’s work [16] proving the formal degree conjecture for regular supercuspidal representations. The main difference between our work and Schwein’s work is that in non-singular case, the Deligne–Lusztig representations can be reducible, and the $S$-groups are not necessarily abelian. Therefore, we have to compare the dimensions of irreducible constituents of the Deligne–Lusztig representations and the dimensions of irreducible representations of $S$-groups.