The strong generic Arthur packet conjecture for GSpin groups

Let FF be a non-Archimedean local field, let ψ\psi be an Arthur parameter for a GSpinGSpin group, let ϕψ\phi_{\psi} be its associated Langlands parameter, and let Π(ϕψ)\Pi(\phi_{\psi}) be the corresponding LL-packet. An LL-packet is tempered when all of its members are tempered representations, and a representation is generic when it has a Whittaker model.

Strong generic Arthur packet conjecture. If Π(ϕψ)\Pi(\phi_{\psi}) has a generic member, then Π(ϕψ)\Pi(\phi_{\psi}) is a tempered LL-packet; equivalently, all members of Π(ϕψ)\Pi(\phi_{\psi}) are tempered.

This strengthens the weak conjecture, which only asserts that the associated Langlands parameter is tempered. The paper states that it establishes this strong version for GSpinGSpin groups under the new local LL-function assumption used in the work.

Sources & referencesView supporting material

Primary source

Yeansu Kim, “Langlands-Shahidi L-functions for GSpin groups and the generic Arthur packet conjecture”, arXiv:1507.07156 (2017).

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