## Abstract

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(N)-invariant R-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix. The second type is associated to a monodromy matrix closely related to the inverse of the monodromy matrix. We show that these two types of Bethe vectors are identical up to normalization and reshu ing of the Bethe parameters. To prove this correspondence we use the current approach. This identity gives new combinatorial relations for the scalar products of the Bethe vectors. The q-deformed case, as well as the superalgebra case, are also evoked in the conclusion.

Original language | English |
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Article number | 44001 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2019 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Apr 2019 |

## Keywords

- Algebraic structures of integrable models
- Integrable spin chains and vertex models
- Quantum integrability (Bethe ansatz)