On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups

Abstract

The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint $\gamma$-factor of its $L$-parameter. In this article, we prove the formal degree conjecture for odd special orthogonal and metaplectic groups in the generic case, which, combined with Arthur’s work on the local Langlands correspondence, implies the conjecture in the nongeneric case.