5 problems

Let $\sigma$ be an automorphic representation and let $r$ be a finite-dimensional representation defining the associated $L$-function. Langlands functoriality conjecture. The $L$-f…

General-type image conjecture. There exists a semisimple group $H$ over $F$ which is a form of $\operatorname{SL}_n$, and there exists a finite extension $L/K$, such that for every…

Global pullback functoriality conjecture. Every, or alternatively at least one, irreducible constituent of $\eta^*\pi$ has L-parameter $\Phi(\eta)\phi$. This is presented as a spec…

Let $E/F$ be a Galois extension of number fields and let $n$ be an integer such that … and, for every divisor $m\mid n$, there are no nontrivial irreducible representations…

Langlands global functoriality conjecture. The representation $\Pi ^{(12)}(\operatorname{GL}_6(F_{\overline\omega }\times_DF_\omega ))$ is nonorthogonally reducible if it decompose…