Plancherel measures for coverings of p-adic SL₂(F)

In these notes, we compute the Plancherel measures associated with genuine principal series representations of n-fold covers of p-adic SL₂. Along the way, we also compute a higher dimensional metaplectic analog of Shahidi local coefficients. Our method involves new functional equations utilizing the Tate γ-factor and a metaplectic counterpart. As an application, we prove an irreducibility theorem.