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We consider $mathfrak{gl}_2$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the actions of the twisted monodromy matrix entries onto twisted off-shell Bethe vectors.
We consider closed XXX spin chains with broken total spin $U(1)$ symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on the modified Bethe vectors. The obtained form
In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $mathcal{E}_{p, gamma}[widehat{mathfrak{gl}_2}]$ as its underlying symmetry algebra. We elaborate on results previously presented by
In this paper, we show that it is always possible to deform a differential equation $partial_x Psi(x) = L(x) Psi(x)$ with $L(x) in mathfrak{sl}_2(mathbb{C})(x)$ by introducing a small formal parameter $hbar$ in such a way that it satisfies the Topolo
We construct a new class of solutions to the dispersionless hyper--CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein--Maxwell cosmological space--time in $(3+1)$--dimensions.
We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian $mathrm Y(mathfrak{gl}_{m|n})$. To a solution we associate a rational difference operator $mathcal D$ and a superspace of rational