Global Weyl module tensor-product conjecture

Let ${\mathfrak g}$ be a simple Lie algebra with fundamental representations $V^{(i)}$, $i=1,\dots,r$, and highest weight vectors $v^{(i)}\in V^{(i)}$. Let $\lambda=\sum_{i=1}^r\lambda_i\omega_i$ be a dominant integral weight. Global Weyl module tensor-product conjecture. The module $W_A(\lambda)$ over ${\mathfrak g}\otimes A$ is isomorphic to the submodule of

$$\left(V^{(1)}\otimes A\right)^{\otimes\lambda_1}\bigotimes\dots\bigotimes\left(V^{(r)}\otimes A\right)^{\otimes\lambda_r}$$

generated by

$$\left(v^{(1)}\otimes1\right)^{\otimes\lambda_1}\bigotimes\dots\bigotimes\left(v^{(r)}\otimes1\right)^{\otimes\lambda_r}.$$

This is presented as an analogue of the cited conjecture about global Weyl modules; the surrounding text verifies the corresponding statement for type $A$ in certain cases, while the assertion for an arbitrary Lie algebra remains conjectural.