Injectivity conjecture for the horizontal quantum affine subalgebra

Let $U_q\,\widehat{\mathfrak{sl}}_{m|n}$ be the quantum affine algebra and let ${\mathcal E}_{m|n}$ be the quantum toroidal algebra. Define $h:U_q\,\widehat{\mathfrak{sl}}_{m|n}\rightarrow {\mathcal E}_{m|n}$ by

$$h(e_i)=E_{i,0},\qquad h(f_i)=F_{i,0},\qquad h(t_i)=K_i\quad (i\in\hat{I}).$$

Its image is $U^{hor}_q\widehat{\mathfrak{sl}}_{m|n}$. Injectivity conjecture. The homomorphism $h:U_q\,\widehat{\mathfrak{sl}}_{m|n}\rightarrow {\mathcal E}_{m|n}$ is injective. In particular, $U^{hor}_q\widehat{\mathfrak{sl}}_{m|n}$ is isomorphic to $U_q\,\widehat{\mathfrak{sl}}_{m|n}$. This identifies the horizontal subalgebra with the quantum affine algebra; the statement is presented as a conjecture, and no resolution is supplied in the source.