Equivalent definitions of Arthur packets for real classical groups

Jeffrey Adams (U of Maryland)

Apr 11. 2022, 14:45 — 15:30

This is joint work with Nicolas Arancibia and Paul Mezo.

Suppose F is a local field of characteristic 0, and G is a reductive group defined over F. Jim Arthur conjectured the existence of sets of representations of G(F)  associated to a map of the Weil-Deligne group of F x SL(2,C) into the L-group of G. These are now known informally as Arthur packets. Arthur gave a construction of these packets for quasisplit classical groups over any field. Adams, Barbasch and Vogan gave a very different construction, for all G, in the case F=R. It has long been expected that the two constructions agree in the cases in which they are both defined: real, quasisplt classical groups. 

This is true (with a small caveat in the case of even orthogonal groups). I will explain the main ingredients of the proof.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Minimal Representations and Theta Correspondence (Workshop)
Wee Teck Gan (U of Singapore)
Marcela Hanzer (U Zagreb)
Alberto Minguez (U of Vienna)
Goran Muic (U Zagreb)
Martin Weissman (UC Santa Cruz)