On Arthur's unitarity conjecture for split real groups

2019/08/12 by Joseph Hundley, Stephen D. Miller, Hundley, Joseph +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Finite Group Theory Research #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1908.04363

openalex publication_date 2019/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On Certain L-Functions

Related

• L-packets and the generic Arthur packet conjectures for even unitary similitude groups
• On the weak local Arthur packets conjecture for split classical groups
• Sur les paquets d'Arthur aux places réelles, translation
• Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups I
• Equivalent definitions of Arthur packets for real unitary groups