On tensor third L-functions of automorphic representations of GL_n(mathbb{A}_F)

Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. We study these problems in a setting related to the Langlands $L$-functions $L(s,\pi,\,\otimes^3),$ where $\pi$ is a cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_F)$ where $F$ is a global field.