Related papers: Bases of Bethe Vectors and Difference Equations wi…
We study integrable models with $\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the Bethe parameters obey some relations weaker…
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(2|1)$ symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe…
The note deals with the Gaudin model associated with the tensor product of n irreducible finite-dimensional sl_{N+1}-modules marked by distinct complex numbers z_1,..., z_n. The Bethe Ansatz is a method to construct common eigenvectors of…
We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum…
We present a method to construct a basis of singular and non-singular common eigenvectors for Gaudin Hamiltonians in a tensor product module of the Lie algebra SL(2). The subset of singular vectors is completely described by analogy with…
We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…
We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the…
We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…
We study quantum integrable GL(3)-based models with a trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation…
We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients.…
We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian $Y({\mathfrak{gl}}_N)$ and the quantum affine algebra…
Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors…
We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra $U_q(\widehat{gl}_N)$ [arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of the product of the transfer matrix and…
We study quantum integrable models with $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. We analyze scalar products of generic Bethe vectors and obtain an explicit representation for them in terms of a sum…
We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by $\mathfrak{gl}(m|n)$ superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their…
Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on…
Heine and Stieltjes in their studies of linear second-order differential equations with polynomial coefficients having a polynomial solution of a preassigned degree, discovered that the roots of such a solution are the coordinates of a…
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…
We discuss the Bethe ansatz in the Gaudin model on the tensor product of finite-dimensional $sl_2$-modules over the field $F_p$ with $p$ elements, where $p$ is a prime number. We define the Bethe ansatz equations and show that if…
We derive a number of results related to the Gaudin model associated to the simple Lie algebra of type G$_2$. We compute explicit formulas for solutions of the Bethe ansatz equations associated to the tensor product of an arbitrary…