Number theory seminar

Number theory seminar by Olivier Taïbi (Imperial)

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

Abstract I will explain the formulation and proof of Arthur's multiplicity formula for automorphic representations of special orthogonal groups and certain inner forms of symplectic groups G over a number field F. I work under an assumption that substantially simplifies the use of the stabilisation of the trace formula, namely that there exists a non-empty set S of real places of F such that G has discrete series at places in S and is quasi-split at places outside S, and restricting to automorphic representations of G(A_F) which have algebraic regular infinitesimal character at the places in S. In particular, this proves the general multiplicity formula for groups G such that F is totally real, G is compact at all real places of F and quasi-split at all finite places of F. Crucially, the formulation of Arthur's multiplicity formula is made possible by Kaletha's recent work on local and global Galois gerbes and their application to the normalisation of Kottwitz-Langlands-Shelstad transfer factors. I will also explain why these particular hypotheses are often enough to handle arithmetic applications.