Jiang–Liu–Shahidi wavefront bound conjecture for Arthur packets

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Let ψ\psi be an Arthur parameter for a reductive group G\mathbf G over a nonarchimedean local field k{\mathsf k}, and let Oψ∨\mathcal O^{\vee}_{\psi} be the nilpotent G∨G^{\vee}-orbit corresponding to the restriction of ψ\psi to SL(2,C)\mathrm{SL}(2,\mathbb C). Jiang–Liu–Shahidi wavefront conjecture. For every X∈ΠψArt(G(k))X\in\Pi^{\mathsf{Art}}_{\psi}(\mathbf G({\mathsf k})), there is a bound

k‾ ⁣WF⁡(X,C)≤d(Oψ∨),{}^{\overline{\mathsf k}}\!\operatorname{WF}(X,\mathbb C)\leq d(\mathcal O^{\vee}_{\psi}),

and this bound is achieved for some X∈ΠψArt(G(k))X\in\Pi^{\mathsf{Art}}_{\psi}(\mathbf G({\mathsf k})). This conjecture extends the formulation known for classical groups to arbitrary reductive groups; its general status is left open in the source.

References

Primary source

Dan Ciubotaru, Lucas Mason-Brown and Emile Okada, “Some Unipotent Arthur Packets for Reductive p-adic Groups”, arXiv:2210.00251 (2022).

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