Unitary principal series of split orthogonal groups

Abstract

We prove the nonunitarity of a large set of parameters for Langlands quotients of minimal principal series of the orthogonal group SO(n+1, n), by showing that the set of unitary principal series parameters of SO(n+1, n) embeds into a (known) union of spherical unitary parameters for certain split orthogonal groups. In an earlier paper, we proved the nonunitarity of the genuine principal series of the metaplectic group Mp(2n) attached to the same set of parameters. We conjecture that the set of parameters is complete in both cases and prove the conjecture for small rank groups and in the case of unipotent parameters.