Bethe Vectors for Orthogonal Integrable Models
Abstract
We consider quantum integrable models associated with the s_{o 3} algebra and describe Bethe vectors of these models in terms of the current generators of the D Y (s_{o 3}) algebra. To implement this program, we use an isomorphism between the Rmatrix and the Drinfeld current realizations of the Yangians and their doubles for classical type B, C, and Dseries algebras. Using these results, we derive the actions of the monodromy matrix elements on offshell Bethe vectors. We obtain recurrence relations for offshell Bethe vectors and Bethe equations for onshell Bethe vectors. The formulas for the action of the monodromy matrix elements can also be used to calculate scalar products in the models associated with the s_{o 3} algebra.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 December 2019
 DOI:
 10.1134/S0040577919110023
 arXiv:
 arXiv:1906.03202
 Bibcode:
 2019TMP...201.1545L
 Keywords:

 Yangian of a simple Lie algebra;
 Yangian double;
 algebraic Bethe ansatz;
 Mathematical Physics;
 High Energy Physics  Theory
 EPrint:
 22 pages