The enhanced Shahidi conjecture for generic members of local Arthur packets
Let be a quasi-split reductive group. A local Arthur packet is a packet of representations attached to a local Arthur parameter, and it is tempered when its parameter has no non-tempered Arthur factor.
Enhanced Shahidi Conjecture. For any quasi-split reductive group , a local Arthur packet is tempered if and only if it has a generic member.
The source says this conjecture is proved assuming the preceding wavefront-set conjecture, and unconditionally for some symplectic and split odd special orthogonal groups. It remains open in the generality stated in the supplied text.
References
Primary source
Baiying Liu and Freydoon Shahidi, “On Jiang's wavefront sets conjecture for representations in local Arthur packets”, arXiv:2603.13465 (2026).
Additional references
5 papers in this index state this conjecture (2022–2026). The statement above is taken from the most recent of them; the others are arXiv:2503.05343, arXiv:2404.07463, arXiv:2209.03816, arXiv:2201.10539.
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