The generic Arthur packet conjecture

Let ψ\psi be an Arthur parameter, let φψ\varphi_{\psi} be its associated Langlands parameter, and let Π(φψ)\Pi(\varphi_{\psi}) be the LL-packet associated to φψ\varphi_{\psi}. A representation is generic with respect to a Whittaker datum if it admits a Whittaker model for that datum. Generic Arthur packet conjecture. If Π(φψ)\Pi(\varphi_{\psi}) has a generic member with respect to some Whittaker datum, then φψ\varphi_{\psi} is tempered. This conjecture has been proved for any quasi-split group under the equality of Langlands–Shahidi and Artin LL-functions, with further progress for classical and general spin groups, but remains open in the stated generality.

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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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