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arXiv · 0904.0922

Uniqueness of Shalika functionals (the Archimedean case)

Avraham Aizenbud·Dmitry Gourevitch·Herve Jacquet
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Abstract

Let F be either R or C. Let $(π,V)$ be an irreducible admissible smooth \Fre representation of GL(2n,F). A Shalika functional $ϕ:V \to \C$ is a continuous linear functional such that for any $g\in GL_n(F), A \in \Mat_{n \times n}(F)$ and $v\in V$ we have $$ ϕ[πg & A 0 & g)v] = \exp(2πi \re(\tr (g^{-1}A))) ϕ(v).$$ 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].

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BibTeXRIS

Avraham Aizenbud, Dmitry Gourevitch, Herve Jacquet. 2009-10-02. Uniqueness of Shalika functionals (the Archimedean case). https://arxiv.org/abs/0904.0922

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