Arthur's Conjectures and the Orbit Method for Real Reductive Groups
Abstract
The first half of this article is expository -- I will review, with examples, the main statements of the Langlands classification and Arthur's conjectures for real reductive groups as formulated by Adams, Barbasch, and Vogan. In the second half, I will turn my attention to the Orbit Method, a conjectural scheme for classifying irreducible unitary representations of a real reductive group. I will give a definition of the Orbit Method in the case when the group is complex. The main input is the theory of unipotent ideals and Harish-Chandra bimodules, developed in arXiv:2108.03453. I will show that the Orbit Method I define is related to Arthur's conjectures via a natural duality map. Finally, I will sketch a possible generalization of this Orbit Method for arbitrary real groups.
Cite
@article{arxiv.2204.04994,
title = {Arthur's Conjectures and the Orbit Method for Real Reductive Groups},
author = {Lucas Mason-Brown},
journal= {arXiv preprint arXiv:2204.04994},
year = {2022}
}
Comments
Article prepared for the Proceedings of the IHES 2022 summer school on the Langlands program. Comments welcome!