Symmetric power functoriality conjecture for RAESDC Hilbert modular representations

Let $n\geq 1$. Let $F^+$ be a totally real field, and let $(\pi,\chi)$ be a RAESDC automorphic representation of $\mathrm{GL}_2({\mathbf A}_{F^+})$ without CM. Symmetric power functoriality conjecture. There exists a RAESDC automorphic representation $(\Pi,\psi)$ of $\mathrm{GL}_n({\mathbf A}_{F^+})$ such that, for every prime $p$ and isomorphism $\iota:\overline{{\mathbf Q}}_p\to{\mathbf C}$,

$$r_\iota(\Pi)\cong\operatorname{Sym}^{n-1}r_\iota(\pi).$$

This is the most general case with $\mathbf K=\emptyset$ of the conjecture attributed in the source to Clozel. It predicts global automorphy of every symmetric power of the associated two-dimensional Galois representation; no resolution is given here.