RESIDUAL SPECTRUM OF SPLIT CLASSICAL GROUPS; CONTRIBUTION FROM BOREL SUBGROUPS

We completely determine the residual automorphic repre-sentations coming from the torus of odd orthogonal groups. Under certain technical assumption on disconnected groups, our results are valid for symplectic groups and even orthog-onal groups. Moeglin has determined the residual spectrum attached to the trivial character of the torus for split classical groups. However, non-trivial characters present some non-trivial difficulties, both local and global. Local problems are resolved in a companion paper with C. Jantzen, where many other useful results are obtained. Introduction. Let F be a number field and A its ring of adeles. Let G be a reductive group defined over F. For simplicity we assume that the center of G is anisotropic over F. A central problem in the theory of automorphic forms is to decompose the right regular representation of G(A) acting on the Hilber