On Arthur's unitarity conjecture for split real groups
arXiv:1908.04363
The paper proves that the Langlands‑specified element of every unipotent Arthur packet for split real groups is unitary, using Eisenstein series, constant‑term formulas and analytic properties of intertwining operators together with basic Dirichlet L‑function inputs.
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 one specified by Arthur) of all unipotent Arthur packets for split real 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. This updated arXiv posting also includes some comments (in blue) concerning statements about normalized intertwining operators we quoted from the literature in Section 9.
34 pages, 1 figure, 3 tables. Post-publication version 3 includes comments (in blue) included to navigate literature statements about normalized intertwining operators