Integrable structure of $\text{BCD}$ conformal field theory and boundary Bethe ansatz for affine Yangian

In these notes we study integrable structures of conformal field theory with $\text{BCD}$ symmetry. We realise these integrable structures as affine Yangian $\mathfrak{g}\mathfrak{l}(1)$ “spin chains” with boundaries. We provide three solutions of Sklyanin $\text{KRKR}$ equation compatible with affine Yangian $R$-matrix and derive Bethe ansatz equations for the spectrum.