ON ARTHUR’S UNITARITY CONJECTURE FOR SPLIT REAL GROUPS

Joseph Hundley, Stephen D. Miller

Research output: Contribution to journalArticlepeer-review

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 crite-rion, 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.

Original languageEnglish (US)
Pages (from-to)1561-1600
Number of pages40
JournalAmerican Journal of Mathematics
Volume144
Issue number6
DOIs
StatePublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics

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