Uniqueness of Shalika functionals (the Archimedean case)

الأصل · EN

Let F be either R or C. Let (π,V) be an irreducible admissible smooth representation of GL(2n,F). A Shalika functional ϕ:V → is a continuous linear functional such that for any g∈ GLₙ(F), A ∈ ₙ × ₙ(F) and v∈ V we have ϕ[πg & A 0 & g)v] = (2πi ((g⁻¹A))) ϕ(v). In this paper we prove that the space of Shalika functionals on V is at most one dimensional. For non-Archimedean F (of characteristic zero) this theorem was proven in [JR].