# On Arthur's unitarity conjecture for split real groups

## TL;DR

This paper proves Arthur's unitarity conjecture for unipotent Arthur packets in split real groups, confirming the unitarity of specific automorphic representations using advanced harmonic analysis and number theory techniques.

## Contribution

It establishes the unitarity of the Langlands element in all unipotent Arthur packets for split real groups, a key step in Arthur's conjectures.

## Key findings

- Proves unitarity of the Langlands element in unipotent Arthur packets
- Uses Eisenstein series and intertwining operators for the proof
- Reduces the problem to a combinatorial analysis involving L-functions

## 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.