## Abstract

We consider quantum integrable models associated with the so_{3} algebra and describe Bethe vectors of these models in terms of the current generators of the DY(so_{3}) 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 so_{3} algebra.

Original language | English |
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Pages (from-to) | 1545-1564 |

Number of pages | 20 |

Journal | Theoretical and Mathematical Physics |

Volume | 201 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Nov 2019 |

## Keywords

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