New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors

Abstract

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-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 the Bethe vectors are identical up to normalization and reshuffling 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.

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Cited by in corpus (6)

• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Bethe vectors for orthogonal integrable models
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• Spinorial R operator and Algebraic Bethe Ansatz
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models
• On the R-matrix realization of the quantum loop algebra. The case of $U_q(D_n^{(2)})$