Higher order Hamiltonians for the trigonometric Gaudin model

Alexander Molev and Eric Ragoucy

Abstract

We consider the trigonometric classical $r$-matrix for ${\mathfrak{gl}}_N$ and the associated quantum Gaudin model. We produce higher Hamiltonians in an explicit form by applying the limit $q\to 1$ to elements of the Bethe subalgebra for the $XXZ$ model.