Gamma Factors of Distinguished Representations of GLₙ(C)

الأصل · EN

Let (π,V) be a GLₙ(R)-distinguished, irreducible, admissible representation of GLₙ(C), let π' be an irreducible, admissible, GLₘ(R)-distinguished representation of GLₘ(C), and let ψ be a non-trival character of C which is trivial on R. We prove that Rankin-Selberg gamma factor at s=1/2 is γ(1/2,π× π'; ψ) = 1. The result follows as a simple consequence from the characterisation of GLₙ(R)-distinguished representations in terms of their Langlands data.