Quantum inverse scattering method and (super)conformal field theory

We consider the possibility of using the quantum inverse scattering method to study the superconformal field theory and its integrable perturbations. The classical limit of the considered constructions is based on the $\widehat{osp}(1|2)$ super-KdV hierarchy. We introduce the quantum counterpart of the monodromy matrix corresponding to the linear problem associated with the L-operator and use the explicit form of the irreducible representations of $\widehat{osp}_q(1|2)$ to obtain the “fusion relations” for the transfer matrices (i.e., the traces of the monodromy matrices in different representations).