Arthur's multiplicity formula for certain inner forms of special orthogonal and symplectic groups

Abstract

Let \mathbf G be a special orthogonal group or an inner form of a symplectic group over a number field F such that there exists a non-empty set S of real places of F at which \mathbf G has discrete series and outside of which \mathbf G is quasi-split. We prove Arthur’s multiplicity formula for automorphic representations of \mathbf G having algebraic regular infinitesimal character at all places in S .