Shahidi's generic cuspidal representation conjecture for symplectic Arthur packets

Let ϕ=i=1r(τi,1)Φ~2(Sp2n)\phi=\boxplus_{i=1}^r(\tau_i,1)\in\widetilde{\Phi}_2({\mathrm{Sp}}_{2n}) be a generic global Arthur parameter. Here Π~ϕ(Sp2n)\widetilde{\Pi}_{\phi}({\mathrm{Sp}}_{2n}) denotes its global Arthur packet, and pm(π)\frak{p}^m(\pi) denotes the set of maximal partitions attached to π\pi. Shahidi's conjecture. There is an irreducible generic cuspidal automorphic representation π\pi of Sp2n(A){\mathrm{Sp}}_{2n}({\mathbb A}) belonging to Π~ϕ(Sp2n)\widetilde{\Pi}_{\phi}({\mathrm{Sp}}_{2n}), and hence

pm(π)={[(2n)]}.\frak{p}^m(\pi)=\{[(2n)]\}.

The conjecture has been proved using the automorphic descent of Ginzburg, Rallis and Soudry.

Sources & referencesView supporting material

Primary source

Dihua Jiang and Baiying Liu, “On cuspidality of global Arthur packets for symplectic groups”, arXiv:1601.01665 (2016).

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