Yangian action conjecture for the twisted affine module ${\cal L}(\Lambda_n)$

Let ${\cal L}(\Lambda_n)$ be the level $1$ integrable module of $A^{(2)}_{2n}$, and let $Y(B_n)$ be the Yangian of type $B_n$. Suppose

$$\operatorname{ch}{\cal L}(\Lambda_n)(q,x)=\sum_{\kappa\in BS}q^{t(\kappa)}s^{\rm L}_{\kappa}(x),$$

where $BS$ is the set of border strips with final part $2n$. Yangian action conjecture. There is a canonical action of $Y(B_n)$ on ${\cal L}(\Lambda_n)$, and the displayed decomposition describes its $Y(B_n)$-module structure. The conjecture extends the preceding character-level expectation from individual border-strip characters to the entire twisted affine module; no proof is supplied in the paper.