Plancherel measures for coverings of p-adic SL(2,F)

Abstract

In these notes we compute the Plancherel measures associated with genuine principal series representations of n-fold covers of p-adic SL(2,F). Along the way we also compute a higher dimensional metaplectic analog of Shahidi local coefficients. Our method involves new functional equations utilizing the Tate Gamma-factor and a metaplectic counterpart. As an application we prove an irreducibility theorem.