The Exterior Cubic L-function of GU(6) and Unitary Automorphic Induction

Abstract

In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\mathrm{GL}}_6\times {\mathrm{GL}}_1$ to that of the quasi-split unitary similitude group ${\mathrm{GU}}_6$ and establish its analytic properties to determine the poles of this $L$-function. Furthermore, we introduce the automorphic induction for automorphic representations of ${\mathrm{GU}}_n$ and then show that the weak Langlands functorial lift for the automorphic induction exists for generic cuspidal automorphic representations. By using this automorphic induction, we give a conjectural criterion on the existence of poles of $L(s,\pi ,{\wedge }^3\otimes \chi )$ for discrete automorphic representations in the tempered spectrum.

44 pages

Cited by in corpus (1)

• Periods of Automorphic Forms Associated to Strongly Tempered Spherical Varieties