Weyl approach to representation theory of reflection equation algebra

The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum groups). We suggest a universal method of constructing finite dimensional irreducible non-commutative representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed which are parametrized by Young diagrams. The spectrum of central elements s(k)=Tr_q(L^k) is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into the direct sum of irreducible components is also suggested.Comment: LaTeX2e file, 27 pages, no figure

Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz

We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe ansatz technique is shown to be equivalent to a chain of successive Backlund transformations "undressing" the original problem to a trivial one.Comment: 22 pages, 2 figures, based on the talk given at the Workshop "Classical and Quantum Integrable Systems", Dubna, January 200

Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]

Tensor operators in graded representations of Z_{2}-graded Hopf algebras are defined and their elementary properties are derived. Wigner-Eckart theorem for irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of tensor operators in the irreducible representation space of Hopf algebra U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the irreducible tensor operators are calculated. A construction of some elements of the center of U_{q}[osp(1\mid 2)] is given.Comment: 16 pages, Late

Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

In this paper, using a Hopf-algebraic method, we construct deformed Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for N=1 case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired $\mathcal{N}=1/2$ SUSY in N=1 non(anti)commutative superspace.Comment: 15 pages, LaTeX. v3:One section added, typos corrected, to appear in Int. J. Mod. Phys.

Reflection KK-matrices related to Temperley-Lieb RR-matrices

The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.Comment: 11 pages, no figures. References added and a few misprints corrected. To appear in Theoretical and Mathematical Physics (2011

Jordanian Quantum Algebra Uh(sl(N)){\cal U}_{\sf h}(sl(N)) via Contraction Method and Mapping

Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\cal U}_{\sf h}(sl(3))$ which has a remarkably simple coalgebraic structure and contains the Jordanian Hopf algebra ${\cal U}_{\sf h}(sl(2))$, obtained by Ohn, as a subalgebra. A nonlinear map between ${\cal U}_{\sf h}(sl(3))$ and the classical $sl(3)$ algebra is then established. In the second part, we give the higher dimensional Jordanian algebras ${\cal U}_{\sf h}(sl(N))$ for all $N$. The Universal ${\cal R}_{\sf h}$-matrix of ${\cal U}_{\sf h} (sl(N))$ is also given.Comment: 17 pages, Late

Paper Session III-B - Prospects of utilization of the space-purpose temperature sensors for public and commercial use

For the temperature monitoring of units, mechanisms and technological manufacture processes use of sensors which convert temperature to electric signal is preferable. Metal and semiconductor resistance thermometers, thermocouples and thermodiodes are such sensors. Comparative characteristics of these sensors are given in Tab. 1. Temperature ranges which are subject to monitoring and control in a number of the most important branches of engineering are represented by Tab. 2. Comparison of these data shows that in majority of cases temperature has to be measured in the range of 190 ¸ 450 K. It appears that thermodiode sensors are the most suitable for this purpose because they are superior to all other sensors in sensitivity, output signal level, cost and simplicity of use. Their salient feature is the possibility of connection with the measuring unit by means of two-wire connection line of length from some tens meters to some kilometers

Critical Behaviour of integrable mixed spins chains

We construct a mixed spin 1/2 and $S$ integrable model and investigate its finite size properties. For a certain conformal invariant mixed spin system the central charge can be decomposed in terms of the conformal anomaly of two single integrable models of spin 1/2 and spin $(S-1/2)$. We also compute the ground state energy and the sound velocity in the thermodynamic limit.Comment: This was the first correct calculation of the central charge in mixed integrable spin chains. For effects of a magnetic field see J.Phys.A:Math.Gen. 26 (1993) 730