On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetry

Abstract

We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from $\mathfrak{g}$, we use the residual $U(1)$ charge and the block Gauss decomposition of the $R$-matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and the AB commutation relation.

- Corrected the statement of Conjecture 6.3, as the order of the tensor product was inconsistent; this correction has been applied throughout. - Added two example calculations after Conjecture 6.3. - Added a table detailing the nesting of Yangian representations for a number of fundamental representations. - Fixed some typos and corrected a broken reference