The $G_{j,\alpha}^{B_n}$ elementary-symmetric-function conjecture

Let $\Theta_j^{B_n}(x,y)$, $1\leq j\leq n$, be the commuting RSM-elements in $YB(B_n)$, and for $\alpha\in\mathbb{Q}$ define

$$G_{j,\alpha}^{B_n}=\left(\Theta_j^{B_n}(x,y)\right)^\alpha-\left(\Theta_j^{B_n}(x,y)\right)^{-\alpha}.$$

The $G_{j,\alpha}^{B_n}$ elementary-symmetric-function conjecture. For every $\alpha\in\mathbb{Q}$,

$$e_j\left((G_{1,\alpha}^{B_n})^2,\ldots,(G_{n,\alpha}^{B_n})^2\right)=0,\qquad 1\leq j\leq n.$$

This is stated as an equivalent formulation of the type $B_n$ Yang–Baxter identity conjecture, so it is likewise unresolved in the source.