On the formal degree conjecture for non-singular supercuspidal representations
arXiv:2106.00878
Abstract
We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein's work 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 -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 -groups.
20 pages