Formal Degrees and Parabolic Induction: the Maximal Generic Case

Abstract

We study the compatibility of the formal degree conjecture and the parabolic induction process in the simplest nontrivial case for quasi-split $p$-adic groups. For a generic discrete series $\ddot{I}€$ induced from an irreducible supercuspidal $\ddot{I}ƒ$ of a maximal Levi subgroup, we compute the quotient $d(\ddot{I}€)/d(\ddot{I}ƒ)$ of formal degrees under some assumptions. As an application, we verify the conjecture for discrete series of split ${\mathrm{G}}_2$ supported on maximal Levi subgroups.