Nested Bethe Ansatz for RTT-Algebra $\mathcal{A}_n$

TL;DR

This paper develops a recursive method to construct Bethe vectors for RTT-algebras of type An, extending previous work on sp(2n) and o(2n) types, advancing the algebraic Bethe ansatz framework.

Contribution

It introduces a new recursive construction of Bethe vectors for RTT-algebras An based on Bethe vectors of lower rank algebras, enhancing the algebraic Bethe ansatz approach.

Findings

Constructed Bethe vectors for RTT-algebra An from those of A_{n-1}

Extended algebraic Bethe ansatz to new algebra classes

Provided a recursive framework for Bethe vector construction

Abstract

This paper continues our recent studies on the algebraic Bethe ansatz for the RTT-algebras of sp($2n$) and o($2n$) types. In these studies, we encountered the RTT-algebras which we called An. The next step in our construction of the Bethe vectors for the RTT-algebras of type sp($2n$) and o($2n$) is to find the Bethe vectors for the RTT-algebras $\mathcal{A}_n$. This paper deals with the construction of the Bethe vectors of the RTT-algebra An using the Bethe vectors of the RTT-algebra $\mathcal{A}_{n-1}$.