The generic Arthur packet conjecture
The generic Arthur packet conjecture
Let be an Arthur parameter, let be its associated Langlands parameter, and let be the -packet associated to . A representation is generic with respect to a Whittaker datum if it admits a Whittaker model for that datum. Generic Arthur packet conjecture. If has a generic member with respect to some Whittaker datum, then is tempered. This conjecture has been proved for any quasi-split group under the equality of Langlands–Shahidi and Artin -functions, with further progress for classical and general spin groups, but remains open in the stated generality.
Sources & referencesView supporting material
Primary source
Yeansu Kim, Muthu Krishnamurthy and Freydoon Shahidi, “L-packets and the generic Arthur packet conjectures for even unitary similitude groups”, arXiv:2506.00892 (2025).
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