Abstract
Let G be the F-rational points of the split group SO2n, where F is a non-Archimedean local field of characteristic 0. In this paper, we give the complete description of the generic dual of G. Based on this result and the local descent result of Jiang and Soudry, we show that the functorial lifting map constructed by Cogdell, Kim, Piatetski-Shapiro and Shahidi is surjective. Along the way, we prove that for any irreducible generic representation σ, if σ ≇ cσ (c an element of O2n(F)\SO2n(F)), then they have the same lifting image and the same twisted local factors, matching Arthur’s current results on local Langlands correspondence. Then, for any local Langlands parameter ϕ of G, we construct a representation σ such that ϕ and σ have the same twisted local factors.
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