Related papers: Scalar products in models with GL(3) trigonometric…
We solve the $A_{2n}^{(2)}$ vertex model with all kinds of diagonal reflecting matrices by using the algebraic Behe ansatz, which includes constructing the multi-particle states and achieving the eigenvalue of the transfer matrix and…
This work is concerned with the formulation of the graded quantum inverse scattering method for a class oflattice models with reflecting boundary conditions. The $sl(2|1)^{(2)}$ and $osp(2|1)$ models are considered with their diagonal…
The Iwahori-Hecke algebra of type A acts on tensor product space of the natural representation of the quantum superalgebra U_q(gl(m,n)). We show this action of the Hecke algebra and the action of U_q(gl(m,n)) on the same space determine…
A new algebraic Bethe ansatz scheme is proposed to diagonalise classes of integrable models relevant to the description of Bose-Einstein condensates in dilute alkali gases. This is achieved by introducing the notion of Z-graded…
In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The associated…
The scalar product of two vectors with $K$ real components can be computed using two quantum channels, that is, information transmission lines in the form of spin-1/2 XX chains. Each channel has its own $K$-qubit sender and both channels…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
We study the category of finite--dimensional bi--graded representations of toroidal current algebras associated to finite--dimensional complex simple Lie algebras. Using the theory of graded representations for current algebras, we…
The first goal of this paper is to give a precise and simple definition for off-shell Bethe vectors in a generic $g$-invariant integrable model for $g=gl_n$, $o_{2n+1}$, $sp_{2n}$ and $o_{2n}$. We prove from our definition that the…
We study the GIT quotients for the diagonal action of the algebraic group $SL_3(\mathbb{C})$ on the $n$-fold product of $\mathbb{P}^2(\mathbb{C})$: in particular we determine a strategy in order to determine the (intersection) Poincar\'{e}…
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…
We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable…
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…
In this work we introduce a notion of tensor product of (twisted) quiver representations with relations in the category of $\mathcal{O}_X$-modules. As a first application of our notion, we see that tensor products of polystable quiver…
We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product…
A product system E over a semigroup P is a family of Hilbert spaces {E_s:s\in P} together with multiplications E_s \times E_t\to E_{st}. We view E as a unitary- valued cocycle on P, and consider twisted crossed products A \times_{\beta,E} P…
We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing…
Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are…
The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…