Formal degree of regular supercuspidals

Abstract

Supercuspidal representations are usually infinite-dimensional, so the size of such a representation cannot be measured by its dimension; the formal degree is a better alternative. Hiraga, Ichino, and Ikeda conjectured a formula for the formal degree of a supercuspidal in terms of its $L$-parameter only. Our first main result is to compute the formal degrees of the supercuspidal representations constructed by Yu. Our second result, using the first, is to verify that Kaletha’s regular supercuspidal $L$-packets satisfy the conjecture.