I have a solution (a $R$ matrix) of the Yang-Baxter equation, \begin{equation} R_{12}(x_{1})R_{13}(x_{1}x_{2})R_{23}(x_{2})=R_{23}(x_{2})R_{13}(x_{1}x_{2})R_{12}(x_{1}) \end{equation}
that probably is associated to the $ U_q[osp(2n+2|2m)^{(2)}]$ Lie superalgebra, but I'm not sure. I would like to certify myself about this. Anybody know how can I proceed?
I know that $ U_q[osp(2n+2|2m)^{(2)}]$ is the orthosymplectic twisted Lie superalgebra, $r=2n+2$ being the number of bosons and $2m$ the number of fermions, however it seems to be very difficult to find any reference of it. The only reference I found, after an extensive search, was the paper of Frappat et Al. named "Structure of basic Lie superalgebras and of their affine extensions", (Commun. Math. Phys. 121,457-500 ,1989), were some information about twisted Lie algebraalgebras was given and I found as well the Dynkin diagrams for the $ U_q[osp(2n+2|2m)^{(2)}]$.
Moreover, for $m=0$ it seems that the Lie superalgebra $ U_q[osp(2n+2|2m)^{(2)}]$ reduces to the $D_{n+1}^{(2)}$$U_q[D_{n+1}^{(2)}]$ classical Lie algebra. In fact, I checked that this $R$ matrix reduces to the Jimbo's $R$ matrix for $m=0$ which is associated to the $D_{n+1}^{(2)}$$U_q[D_{n+1}^{(2)}]$ Lie algebra. I'm also interested in the special case $n=0$, that is, the $ U_q[osp(2|2m)^{(2)}]$ Lie algebra.
Can anyboby give some expanation of these issues, or indicate some reference related to? I will be very tankful for any help. Thank you in advance!
