On tensor third $L$-functions of automorphic representations of ${\mathrm{G}\mathrm{L}}_n({\mathbb{A}}_F)$

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 ${\mathrm{G}\mathrm{L}}_n({\mathbb{A}}_F)$ where $F$ is a global field.