Bethe Vectors for Orthogonal Integrable Models

A. N. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We consider quantum integrable models associated with the so3 algebra and describe Bethe vectors of these models in terms of the current generators of the DY(so3) algebra. To implement this program, we use an isomorphism between the R-matrix and the Drinfeld current realizations of the Yangians and their doubles for classical type B-, C-, and D-series algebras. Using these results, we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We obtain recurrence relations for off-shell Bethe vectors and Bethe equations for on-shell 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 so3 algebra.

Original languageEnglish
Pages (from-to)1545-1564
Number of pages20
JournalTheoretical and Mathematical Physics
Issue number2
Publication statusPublished - 1 Nov 2019


  • algebraic Bethe ansatz
  • Yangian double
  • Yangian of a simple Lie algebra


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