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arXiv · 2204.04994

Arthur's Conjectures and the Orbit Method for Real Reductive Groups

Lucas Mason-Brown
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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.

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Lucas Mason-Brown. 2022-04-11. Arthur's Conjectures and the Orbit Method for Real Reductive Groups. https://arxiv.org/abs/2204.04994

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