Unitary Dual Conjecture for General Reductive Groups (Conjecture 5.12)

Establish that, for any connected reductive group G defined over a p-adic field for which the theory of local Arthur packets is available, the closure Π_A(G) of Arthur representations equals the full unitary dual Π_u(G).

Background

Extending Conjecture 1.1 beyond classical groups, the authors propose that the closure of Arthur-type packets should exhaust the entire unitary dual for any connected reductive p-adic group once Arthur’s endoscopic classification is in place.

They provide supporting examples (e.g., exceptional group G2) and discuss why realizing the unitary dual through Arthur-theoretic constructions would yield computable algorithms for representation classification.

References

Conjecture 5.12. Let G be a connected reductive group defined over a p-adic field. If the theory

of local Arthur packets as conjectured in [Art89] is valid, then the equality Π (G) =AΠ (G) holus.

— Arthur representations and unitary dual for classical groups (2410.11806 - Hazeltine et al., 15 Oct 2024) in Conjecture 5.12, Section 5