Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian

In these notes we study integrable structures of conformal field theory with BCD symmetry. We realise these integrable structures as gl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{gl} $$\end{document}(1) affine Yangian “spin chains” with boundaries. We provide three solutions of Sklyanin KRKR equation compatible with the affine Yangian R-matrix and derive Bethe ansatz equations for the spectrum. Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras.