On the residual spectrum of split classical groups supported in the Siegel maximal parabolic subgroup

Abstract

For the split symplectic and special orthogonal groups over a number field, we decompose the part of the residual spectrum supported in the maximal parabolic subgroup with the Levi factor isomorphic to GL n . The decomposition depends on the analytic properties of the symmetric and exterior square automorphic L-functions, but seems sufficient for the computation of the corresponding part of the Eisenstein cohomology. We also prove that if one assumed Arthur’s conjectural description of the discrete spectrum for the considered groups, then one would be able to find the poles of the L-functions in question, and would make the decomposition more precise.