The Suzuki functor conjecture on extension algebras

Let $\boldsymbol{c}$ denote the critical level, let $\mathsf{F}_{\mathbf{c}}$ be the Suzuki functor, and let $\mathbb{W}_{\mathbf{c}}(\lambda)$ and $\Delta_0(\lambda)$ be the corresponding Weyl and standard modules for $\lambda\in\mathcal{P}(n)$. Write $\operatorname{Ext}^\bullet$ for the graded extension algebra. The Suzuki functor conjecture on extension algebras. The functor $\mathsf{F}_{\mathbf{c}}$ induces a surjective algebra homomorphism

$$\operatorname{Ext}_{\widehat{\mathbf{U}}_{\mathbf{c}},G[[t]]}^\bullet(\mathbb{W}_{\mathbf{c}}(\lambda),\mathbb{W}_{\mathbf{c}}(\lambda))\longrightarrow \operatorname{Ext}_{\mathcal{H}_{0}}^\bullet(\Delta_0(\lambda),\Delta_0(\lambda)),$$

which is given by restriction of differential forms via the inclusion referred to in the source. Frenkel and Teleman conjecture that the source extension algebra is the algebra of differential forms on $\operatorname{Op}_{\check{G}}^\lambda(\mathbb{D})$, while the target is identified with differential forms on the corresponding Schubert cell; the proposed map is the restriction between these spaces. The statement is presented as a conjectural geometric strengthening of the known degree-one map, and its general validity remains open.