Local Intertwining Relations and Co-tempered $A$-packets of Classical Groups
Abstract
The local intertwining relation is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. We prove several instances of the local intertwining relation for quasi-split classical groups and the twisted general linear group, as they are required in the inductive proof of the endoscopic classification for quasi-split classical groups due to Arthur and Mok. In addition, we construct the co-tempered local -packets by Aubert duality and verify their key properties by purely local means, which provide the seed cases needed as an input to the inductive proof. Together with further technical results that we establish, this makes the endoscopic classification conditional only on the validity of the twisted weighted fundamental lemma.
Cite
@article{arxiv.2410.13504,
title = {Local Intertwining Relations and Co-tempered $A$-packets of Classical Groups},
author = {Hiraku Atobe and Wee Teck Gan and Atsushi Ichino and Tasho Kaletha and Alberto Mínguez and Sug Woo Shin},
journal= {arXiv preprint arXiv:2410.13504},
year = {2025}
}
Comments
Several arguments were refined. Appendix F was added