On the local Langlands conjectures for disconnected groups
Representation Theory
2026-05-19 v2 Number Theory
Abstract
We extend the local Langlands conjectures to a certain class of disconnected groups, allowing non-abelian component groups, and recast in this language some aspects of twisted endoscopy. We further introduce normalized twisted transfer factors and a normalized correspondence between an -packet for a disconnected group and the set of representations of the centralizer groups of its Langlands parameter. We prove the first instance of this conjecture, in which the identity component of the (possibly non-abelian) disconnected group is a torus.
Keywords
Cite
@article{arxiv.2210.02519,
title = {On the local Langlands conjectures for disconnected groups},
author = {Tasho Kaletha},
journal= {arXiv preprint arXiv:2210.02519},
year = {2026}
}
Comments
Second updated version. Changes since v1: Changed handling of Kottwitz signs to align with results for real groups, added material about admissible Whittaker data and toral invariants, added appendices