Feigin–Loktev fusion-product independence conjecture

Let $\mathfrak{g}$ be a simple Lie algebra, let $k\in\mathbb{Z}_{>0}$, and let $\lambda_s\in P^+$ for $1\leq s\leq k$. For pairwise distinct complex numbers $a_1,\ldots,a_k$ and pairwise distinct complex numbers $b_1,\ldots,b_k$, write $V_a(\lambda)$ for the evaluation module with parameter $a$, and let

$$V_{a_1}(\lambda_1)*\cdots*V_{a_k}(\lambda_k)$$

denote their fusion product, the associated graded $\mathfrak{g}[t]$-module of the filtered tensor product. Feigin–Loktev fusion-product independence conjecture. One has an isomorphism of $\mathfrak{g}[t]$-modules

$$V_{a_1}(\lambda_1)*\cdots*V_{a_k}(\lambda_k)\cong V_{b_1}(\lambda_1)*\cdots*V_{b_k}(\lambda_k).$$

The conjecture asserts that, for finite-dimensional irreducible representations, the fusion product is independent of the distinct evaluation points. The paper proves a significant case of this conjecture, while the stated general form is not resolved here.