Generalized Formal Degree

Let G be a reductive group over a local field of characteristic zero or a finite central cover of such a group. We present a conjecture that enables one to define formal degree for all unitary representations of G. The conjecture is proved for GLn and $\widetilde {SL}_2$ over real and p-adic fields, together with a formal degree relation concerning the local theta correspondence between $\widetilde {SL}_2$ and SO3.