Joint IAS/PU Number Theory

The local intertwining relation (LIR) is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. It plays a central role in Arthur’s endoscopic classification for quasi-split classical groups. In this talk, I will discuss some seed theorems on LIR needed to complete Arthur's work, focusing on one of them: how to extend LIR from the tempered case to the case of non-tempered Arthur packets via Aubert duality (a.k.a. Aubert-Zelevinsky involution). Based on joint work with Hiraku Atobe, Wee Teck Gan, Atsushi Ichino, Tasho Kaletha, and Alberto Minguez.