Shahidi's generic cuspidal representation conjecture for symplectic Arthur packets

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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.

References

Primary source

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

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