Plancherel measures for coverings of p-adic SL(2,F) (1411.6134v2)

Published 22 Nov 2014 in math.NT

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.

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