The geometric and algebraic R-matrix correspondence for the rank-one Fock space

Let $R_{1,1}$ be the endomorphism of the tensor product of the two Fock spaces $4\Lambda_{\mathbb{F}}(u_1) \otimes \Lambda_{\mathbb{F}}(u_2)4$ over $4\mathbb{F}_24$, and let $R(u_2/u_1)$ denote the $R$-matrix in the cited Fock-space representation.

R-matrix correspondence conjecture. The endomorphism

$$R_{1,1} \in \operatorname{End}_{\mathbb{F}_2}\left(\Lambda_{\mathbb{F}}(u_1) \otimes \Lambda_{\mathbb{F}}(u_2)\right)$$

matches $R(u_2/u_1)$.

The conjecture asserts that the geometric stable-basis construction produces the same operator as the $R$-matrix of the quantum toroidal algebra. The source describes the required choices of stable-basis data as part of the conjecture; no resolution is supplied here.