Title: The characterization of theta-distinguished representations of GL(n)
Speaker: Eyal Kaplan
Abstract: Consider a pair of exceptional representations in the sense of Kazhdan and Patterson, of a metaplectic double cover of GL(n). The tensor of these representations is a (very large) representation of GL(n). We characterize it 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 exceptional representations. As a corollary, an exceptional representation is shown to admit a new "metaplectic Shalika model."
Seminar URL: https://research.math.osu.edu/reps/
