arXiv subjects

O. Navratil

Publications and source records attributed to O. Navratil.

8 recordsLinked to original sources

arXiv2020

Nested Bethe Ansatz for RTT-Algebra $\mathcal{A}_n$

This paper continues our recent studies on the algebraic Bethe ansatz for the RTT-algebras of sp($2n$) and o($2n$) types. In these studies, we encountered the RTT-algebras which we called An. The next step in our construction of the Bethe vectors for the RTT-algebras of type sp($2n$) and o($2n$) is to find the Bethe vectors for the RTT-algebras $\mathcal{A}_n$. This paper deals with the construction of the Bethe vectors of the RTT-algebra An using the Bethe vectors of the RTT-algebra $\mathcal{A}_{n-1}$.

math-ph↗

arXiv2019

Nested Bethe Ansatz for RTT Algebra of U_q(sp(2n) Type

We study the highest weight representations of the RTT algebras for the R matrix of sp_q(2n) type by the nested algebraic Bethe ansatz. It is a generalization of our study for R matrix of sp(2n) and so(2n) type

math-ph↗

arXiv2015

Remarks towards the spectrum of the Heisenberg spin chain type models

The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two--component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is consedered. Finally, we discuss some questions relating to the general open Hecke chain models.

math-ph↗

arXiv2008

New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

We 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 $| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>$, where $w_1$, $w_2$ fulfil the standard well-know Bethe Ansatz equations.

math-ph↗

arXiv2003

The $q$-boson-fermion realizations of quantum suprealgebra $U_q(gl(2/1))$

We show that our construction of realizations for Lie algebras and quantum algebras can be generalized to quantum superalgebras, too. We study an example of quantum superalgebra $U_q(gl(2/1))$ and give the boson-fermion realization with respect to one pair od q-deformed boson operator and 2 pairs of fermions.

math.QA↗

arXiv2002

On the Fock Space Realizations of Nonlinear Algebras Describing the High Spin Fields in AdS Spaces

The method of construction of Fock space realizations of Lie algebras is generalized for nonlinear algebras. We consider as an example the nonlinear algebra of constraints which describe the totally symmetric fields with higher spins in the AdS space-time.

hep-th↗

arXiv2000

Nonlinear Superposition Formulas Based on Lie Group SO(n+1,n)

Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear superposition formulas. These systems are connected with local Lie groups tranformations on their homogeneous spaces. In the presented work the nonlinear superposition formulas are constructed for the case of the SO(3,2) group and some aspects in the general case of SO(n+1,n) are studied.

nlin.SI↗

arXiv1992

The q-Boson Realizations of the Quantum Group $U_{q}(sl(n+1,C))$

We give explicit expression of recurrency formulae of canonical realization for quantum enveloping algebras $U_{q}(sl(n+1,C))$. In these formulas the generators of the algebra $U_{q}(sl(n+1,C))$ are expressed by means of n-canonical q-boson pairs one auxiliary representation of the algebra $U_{q}(gl(n,C))$.

hep-th↗