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.