The weak generic Arthur packet conjecture for GSpin groups

Let FF be a non-Archimedean local field, let H\textbf{H} be a quasi-split reductive group over FF, and let ψ\boldsymbol{\psi} be an Arthur parameter with associated Langlands parameter ϕψ\phi_{\psi}. Write Π(ϕψ)\Pi(\phi_{\psi}) for the LL-packet attached to ϕψ\phi_{\psi}. A representation in an LL-packet is generic if it has a Whittaker model, and a Langlands parameter is tempered if its image in the dual group is bounded.

Weak generic Arthur packet conjecture. If Π(ϕψ)\Pi(\phi_{\psi}) has a generic member, then the Langlands parameter ϕψ\phi_{\psi} is tempered.

The conjecture is the converse direction to the tempered LL-packet conjecture in the setting of Arthur parameters. The paper states that its main theorem proves this weak version for GSpinGSpin groups, so the claim is solved in that case.

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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