On the Local Converse Theorem for p-adic GLn
In this paper, we completely prove a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field.
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arXiv subjects
Herve Jacquet
Publications and source records attributed to Herve Jacquet.
A remark on a converse theorem of Cogdell and Piatetski-Shapiro
In this paper, we reprove a global converse theorem of Cogdell and Piatetski-Shapiro using purely global methods.
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Uniqueness of Shalika functionals (the Archimedean case)
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].
math.RT↗