Cyclotomic Gaudin Models: Construction and Bethe Ansatz

To any finite-dimensional simple Lie algebra ({mathfrak{g}}) and automorphism ({sigma: mathfrak{g}to mathfrak{g}}) we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of ({U(mathfrak{g})^{otimes N}}) generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case ({sigma ={rm id}}).