Shahidi’s enhanced genericity conjecture

Determine whether, for any connected reductive p-adic group G and any Arthur parameter ψ, the Arthur packet Π_ψ(G) contains a generic representation if and only if ψ is tempered.

Background

Shahidi’s enhanced genericity conjecture strengthens earlier expectations linking temperedness of parameters to genericity in packets. In the framework of ABV-packets and under partial confirmations of Arthur’s conjectures, the authors show that their geometric results imply this enhanced genericity when Vogan’s conjecture holds in one inclusion.

The conjecture remains a central open direction in the theory of local Arthur packets, connecting deep harmonic-analytic properties (generic Whittaker models) with arithmetic information encoded by Arthur parameters.