A New Basis For Bethe Vectors Of The Heisenberg Model

We present a detailed construction of a completely symmetric representation of the monodromy matrix by the use of Drinfel’d twists for the rational $sl(3)$ Heisenberg model without refering to the special symmetry of the model. With the help of this representation we are able to resolve the hierarchy of the nested Bethe wavevectors for the $sl(3)$ invariant rational Heisenberg model.