Related papers: Combinatorial Formulae for Nested Bethe Vectors
We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In particular, we prove that the tensor product of fundamental…
By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…
The U_q(\hat{sl}(2)) Bethe equation is studied at q=0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and…
We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting…
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…
Using the fusion product of the representations of the Lie algebra $\mathfrak{sl}_2$ we construct a set of the integrable highest weight $\hat{\mathfrak{sl}_2}$-modules $L^D$, depending on the vector $D\in\mathbb{N}^{k+1}$. In a special…
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…
The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted…
This short note corresponds to a talk given at "Lie Theory and Its Applications in Physics", (Varna, Bulgaria, June 2013) and is based on joint works with S. Belliard, S. Pakuliak and N. Slavnov, see arXiv:1206.4931, arXiv:1207.0956,…
We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda, the weight subspace of weight $\lambda$ of the tensor product of k polynomial irreducible gl_N-modules with highest weights…
We study quantum integrable models with GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of the highest…
In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the…
We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for quantum…
We shall derive Kazhdan-Lusztig type character formula for the irreducible modules with arbitrary non-critical highest weights over affine Lie algebras from the rational case by using the translation functor, the Enright functor and…
A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly. (Part II of…
This work is part of a project on weight bases for the irreducible representations of semisimple Lie algebras with respect to which the representation matrices of the Chevalley generators are given by explicit formulas. In the case of sl_n,…
We consider a generalized model with SU(3)-invariant R-matrix, and review the nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum formula for the scalar product between generic Bethe vectors, originally obtained…
We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining…
The Yang-Baxterization R(z) of the trigonometric R-matrix is computed for the two-parameter quantum affine algebra of type A. Using the fusion procedure we construct all fundamental representations of the quantum algebra as wedge products…
Using Functional Bethe Ansatz technique, factorizing Drinfel'd Twists for any finite dimensional irreducible representations of the Yangian Y(sl(2)) are constructed.