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 $S$.