Fourier–Dumitrescu fusion-product conjecture for restricted local Weyl modules

Let $W_1,\dots,W_r$ be the modules considered in the preceding construction, let $\mathcal{A}(\lambda_1,\dots,\lambda_r)$ be the associated parameter algebra, and let $\mathbb{C}_0$ denote its quotient by the maximal ideal corresponding to $0$. Then

$$R(W_1,\dots,W_r)\otimes_{\mathcal{A}(\lambda_1,\dots,\lambda_r)}\mathbb{C}_0$$

is a $\mathfrak{g}[t]$-module. Fourier–Dumitrescu conjecture. This module is isomorphic to the fusion product of the modules $W_i(c_i)$ for $(c_1,\dots,c_r)$ in some Zariski open subset of $\mathbb{C}^r$. The conjecture is presented as a generalization of known results for local Weyl modules; the source gives no resolution, so it remains open.