Feigin's two-factor defining-relations conjecture

Let $cmathfrak{g}$ be a semisimple complex Lie algebra, let $P^+$ denote its dominant integral weights, and fix $clambda_1,clambda_2in P^+$. Put $clambda=clambda_1+clambda_2$, and let $I(clambda_1,clambda_2)$ be the left ideal in $U(cmathfrak{g}cotimescmathbb C[t])$ generated by the relations listed in the source. For distinct $a_1,a_2incmathbb C$, form the fusion product of the evaluation modules. Feigin's two-factor conjecture. There is an isomorphism of graded $cmathfrak{g}cotimescmathbb C[t]$-modules

$$V(clambda_1)_{a_1}cast V(clambda_2)_{a_2}\cong U(cmathfrak{g}cotimescmathbb C[t])/I(clambda_1,clambda_2).$$

This is the concrete form of Feigin's defining-relations conjecture; the supplied text does not state a general resolution.