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

TL;DR

This paper proves Arthur's multiplicity formula for automorphic representations of certain special orthogonal and symplectic groups over number fields, focusing on those with specific real place properties and algebraic regular infinitesimal characters.

Contribution

It establishes Arthur's multiplicity formula for a class of inner forms of special orthogonal and symplectic groups with particular local conditions.

Findings

Proves Arthur's multiplicity formula for specified groups.

Handles cases with discrete series at real places.

Addresses automorphic representations with algebraic regular infinitesimal characters.

Abstract

Let 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 G has discrete series and outside of which G is quasi-split. We prove Arthur's multiplicity formula for automorphic representations of G having algebraic regular infinitesimal character at all places in S.