The enhanced Shahidi conjecture for generic members of local Arthur packets

Let GG 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 GG, 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.

Sources & referencesView supporting material

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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