4 problems

Let $O_p(D_n)$ act on the two parity spaces $V_+$ and $V_-$, and let $K_{1,2}(z)$ and $K_{2,2}(z)$ be the associated affine $K$-matrices. For even $n$, let $Z_l^\pm$ (…

Let $O_p(B_n)$ be the classical Onsager algebra acting on the representation space $V$, and let $K_{1,1}(z)$ and $K_{2,1}(z)$ be the two commuting affine $K$-matrices compatible wi…

Let $O_p(A_{n-1})$ be the classical subalgebra of the Onsager algebra $O_p(A^{(1)}_{n-1})$, and let $V_l$ ($0\le l\le n$) be the representation spaces of the representations…

Generalized Onsager presentation conjecture. The Lie algebra $\widetilde{\mathfrak k}$ is isomorphic to $\mathfrak k$.