Injectivity conjecture for homomorphisms between global Weyl modules

Let $A=\mathcal R_{k,\ell}$ for some $k,\ell\in\mathbb Z_+$. For $\bos=(s_1,\ldots,s_n)\in\mathbb Z_+^n$, let $W_A(\bos)$ denote the corresponding global Weyl module, and let $P^+$ be the set of dominant integral weights. Injectivity conjecture. For all $\lambda\in P^+$ and $\bos\in\mathbb Z_+^n$, any non-zero element of

$$\operatorname{Hom}_{\mathfrak{g}\otimes A}(W_A(\lambda),W_A(\bos))$$

is injective. This conjecture extends the preceding injectivity result for endomorphisms and the stated special cases of homomorphisms between global Weyl modules; its validity in the generality above is left open.