Semi-infinite fusion conjecture for affine highest-weight modules

Let $\widehat{\mathfrak{g}}$ be an affine Kac–Moody algebra, let $\Lambda=m\Lambda_0+\lambda$ be a dominant integral weight, and let $V(\Lambda)$ and $V(\lambda)$ denote the corresponding highest-weight modules. Semi-infinite fusion conjecture.

$$V(\Lambda)\simeq\underset{n\rightarrow\infty}{\operatorname{lim}}\,D(m,\Theta)\ast\cdots\ast D(m,\Theta)\ast V(\lambda)$$

as ${\mathcal{C}\mathfrak{g}}$-modules. This generalizes the preceding semi-infinite fusion realization of $V(m\Lambda_0)$; the source gives no resolution.