Introduction to the Algebraic Bethe Ansatz

Leon A. Takhtajan

James Plunkett

Ferenc Woynarovich

Michael Karabach, Gerhard H. Muller, Harvey Gould +1 more

Bill Sutherland

Nikita Slavnov

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a \mathfrak{gl}_3 𝔤 𝔩 3 -invariant R R -matrix as the basic example, however, we also describe possible generalizations. We give recursions and explicit formulas for the Bethe vectors. We also give a representation for the Bethe vectors in the form of a trace formula.