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

For the split symplectic and special orthogonal groups over a number field, the part of the residual spectrum supported in the maximal parabolic subgroup with the Levi factor isomorphic to general linear group is decomposed. 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.

symplectic group; special orthogonal group; number field; Eisenstein cohomology

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