6 problems

Let ${\cal BE}(G_2)$ be the bracket algebra of type $G_2$, and let $\Theta_1,\Theta_2$ be the corresponding RSM-elements; let $\phi_1$ and $\phi_2$ denote the two polynomial expres…

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

Let $YB(B_n)$ be the Yang–Baxter algebra generated by the elements $h_{ij}(x)$, $g_{ij}(x)$, and $h_j(y)$, and let $\Theta_j^{B_n}(x,y)$, $1\leq j\leq n$, be the associated commuti…

Let ${\cal BE}(B_n)$ be the modified bracket algebra of type $B_n$, and let $\Theta_j(x,y)^{B_n}$, $1\leq j\leq n$, be the commuting RSM-elements defined in the associated Yang–Bax…

Consider the braided Yang–Baxter algebra obtained by discretizing and quantizing the monodromy matrices of two coupled modified Korteweg–de Vries equations, and take its cylinder c…

Let $T_{1}^{(K)}(\lambda)$ be the transfer matrix of the general $gl_{1|2}$-graded Yang–Baxter algebra with twisted boundary conditions. Let $t_{1}(\lambda \mid \{x_a\})$ be the po…