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

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 ${\mathcal{A}}_{n-1}$.

32 pages