The characterization of theta-distinguished representations of $GL_n$

Let $θ$ and $θ'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $θ\otimesθ'$ is a (very large) representation of $GL_n$. We characterize its irreducible generic quotients. In the square-integrable case, these are precisely the representations whose symmetric square L-function has a pole at s=0. Our proof of this case involves a new globalization result. In the general case these are the representations induced from distinguished data or pairs of representations and their contragradients. The combinatorial analysis is based on a complete determination of the twisted Jacquet modules of $θ$. As a corollary, $θ$ is shown to admit a new "metaplectic Shalika model".

No reviews yet.

No comments yet.