Geometric structure and the local Langlands conjecture
Representation Theory
2013-05-21 v3 Number Theory
Abstract
We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive -adic group. The method of proof is to establish the presence of a very simple geometric structure, in both the smooth dual and the Langlands parameters. We prove that this geometric structure is present, in the same way, for the general linear group, including all of its inner forms. With these results as evidence, we give a detailed formulation of a general geometric structure conjecture.
Cite
@article{arxiv.1211.0180,
title = {Geometric structure and the local Langlands conjecture},
author = {Anne-Marie Aubert and Paul Baum and Roger Plymen and Maarten Solleveld},
journal= {arXiv preprint arXiv:1211.0180},
year = {2013}
}
Comments
75 pages. Some minor changes and corrections have been made