The doubling integral for the principal series of [formula omitted] and [formula omitted

Abstract

In a previous article, we explicitly computed the doubling integral for constituents of the unramified principal series for Sp 2 ( F ) and Sp ˜ 2 ( F ) . Those computations relied on some intermediate constructions related to the theory of local theta liftings that make generalizing the computations to higher rank groups or more ramified representations quite difficult. This article attempts to compute the doubling integral for arbitrary constituents of the (possibly ramified) principal series representations for arbitrary rank symplectic and metaplectic groups. To do this, we circumvent the intermediate computations from the previous article, avoid constructions relying on the theory of local theta lifts, and interpret the integration over various unipotent subgroups as standard intertwining operators. We would also like to thank the referees for their careful reading of this manuscript as well as their suggestions for its improvement.