On Arthur's unitarity conjecture for split real groups

Abstract

abstract:Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the ``Langlands element'' (i.e., the representation specified by Arthur) of all unipotent Arthur packets for split real exceptional groups. The proof uses Eisenstein series, Langlands' constant term formula and square integrability criterion, analytic properties of intertwining operators, and some mild arithmetic input from the theory of Dirichlet $L$-functions, to reduce to a more combinatorial problem about intertwining operators.