Jordanian deformation of the open $s\ell(2)$ Gaudin model

We derive a deformed $s\ell(2)$ Gaudin model with integrable boundaries. Starting from the Jordanian deformation of the $SL(2)$-invariant Yang $R$-matrix and generic solutions of the associated reflection equation and the dual reflection equation, we obtain the corresponding inhomogeneous spin-$1/2$ XXX chain. The semiclassical expansion of the transfer matrix yields the deformed $s\ell(2)$ Gaudin Hamiltonians with boundary terms.