O. Navrátil

A method for construction of the matrix solvable models

We give a method for construction of the solvable models. The method is based on an idea of Turbiners to transform the Hamiltonian into a simple solvable form. This method gives a possibility of constructing some matrix models. We apply this method to the models of the Calogero type and obtain solvable models of the three-particle system with the matrix 2 × 2 potential, which was constructed by Polychronakos, and a new model with the matrix 3 × 3 potential.

New formula for the eigenvectors of the Gaudin model in the sl(3) case

AbstractWe propose new formulas for eigenvectors of the Gaudin model in the sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula

THE ADJOINT REPRESENTATION OF QUANTUM ALGEBRA Uq(sl(2))

\left| {w_1 ,w_2 )} \right. = \sum\limits_{n = 0}^\infty {\frac{{P^n }} {{n!}}} \left| {w_1 ,w_2 ,0} \right\rangle ,

Spin Chain Models of Free Fermions

where w1, w2 fulfil the standard well-know Bethe Ansatz equations.

Extremal vectors for Verma-type representations of su(2, 2)

We give the solution to the problem of normal ordering of monomials (a+a)n in pairs of deformed annihilation and creation operators of the Heisenberg algebra involving the reflection operator.

EXTREMAL VECTORS FOR VERMA TYPE REPRESENTATION OF B2

Starting from any representation of the Lie algebra on the finite dimensional vector space V we can construct the representation on the space Aut(V). These representations are of the type of ad. That is one of the reasons, why it is important to study the adjoint representation of the Lie algebra on the universal enveloping algebra U(). A similar situation is for the quantum groups Uq(). In this paper, we study the adjoint representation for the simplest quantum algebra Uq(sl(2)) in the case that q is not a root of unity.

7th International Conference on Quantum Theory and Symmetries (QTS7)

We give explicit realization for the quantum enveloping algebras Uq(Bn). In these formulae the generators of the algebra are expressed by means of 2n−1 canonical q-boson pairs and one auxiliary representation of Uq(Bn−1)

Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

We consider the integrable open spin chain models formulated through the generators of the Hecke algebras which are realized in terms of free fermions.