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Local Intertwining Relations and Co-tempered $A$-packets of Classical Groups

Authors :
Atobe, Hiraku
Gan, Wee Teck
Ichino, Atsushi
Kaletha, Tasho
Mínguez, Alberto
Shin, Sug Woo
Publication Year :
2024

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 $A$-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.<br />Comment: 190 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2410.13504
Document Type :
Working Paper