Plancherel measures for coverings of \(p\)-adic \(\mathrm{SL}_2(F)\) (Q2828368)

From the abstract: ``In these notes, we compute the Plancherel measures associated with genuine principal series representations of \(n\)-fold covers of \(p\)-adic \(\mathrm{SL}(2)\). 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.''NEWLINENEWLINEThe paper consists mainly of lengthy computations. Sections 1--3 recall definitions, section 4 computes the intertwining operator, section 5 computes the Plancherel measure and discusses reducibility of parabolically induced representations. An appendix reproduces unpublished computations of Sweet.