Y(so(5)) symmtry of the nonlinear Schro¨\ddot{o}dinger model with four-cmponents

The quantum nonlinear Schr$\ddot{o}$dinger(NLS) model with four-component fermions exhibits a $Y(so(5))$ symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel'd formula and furthermore, the $RTT$ relation with the general form of rational R-matrix given by Yang-Baxterization associated with $so(5)$ algebraic structure.Comment: 10 pages, no figure

Integrals of motion of the Haldane Shastry Model

In this letter we develop a method to construct all the integrals of motion of the $SU(p)$ Haldane-Shastry model of spins, equally spaced around a circle, interacting through a $1/r^2$ exchange interaction. These integrals of motion respect the Yangian symmetry algebra of the Hamiltonian.Comment: 13 pages, REVTEX v3.

Super Yangian Double DY(gl(1∣1))DY( gl(1|1)) and Its Gauss Decomposition

We extend Yangian double to super (or graded) case and give its Drinfel'd generators realization by Gauss decomposition.Comment: 6 pages, Latex, no figure

The structure of quantum Lie algebras for the classical series B_l, C_l and D_l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys. A. Minor misprints in eqs. 5.11 and 5.12 correcte

Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic gl(N) open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to the calculation of the transfer matrix eigenvalues.Comment: 1

A central extension of \cD Y_{\hbar}(\gtgl_2) and its vertex representations

A central extension of \cD Y_{\hbar}(\gtgl_2) is proposed. The bosonization of level $1$ module and vertex operators are also given.Comment: 10 pages, AmsLatex, to appear in Lett. in Math. Phy

Factorizing twists and R-matrices for representations of the quantum affine algebra U_q(\hat sl_2)

We calculate factorizing twists in evaluation representations of the quantum affine algebra U_q(\hat sl_2). From the factorizing twists we derive a representation independent expression of the R-matrices of U_q(\hat sl_2). Comparing with the corresponding quantities for the Yangian Y(sl_2), it is shown that the U_q(\hat sl_2) results can be obtained by `replacing numbers by q-numbers'. Conversely, the limit q -> 1 exists in representations of U_q(\hat sl_2) and both the factorizing twists and the R-matrices of the Yangian Y(sl_2) are recovered in this limit.Comment: 19 pages, LaTe

Soliton cellular automaton associated with G2(1)G_2^{(1)} crystal base

We calculate the combinatorial $R$ matrix for all elements of $\mathcal{B}_l\otimes \mathcal{B}_1$ where $\mathcal{B}_l$ denotes the $G_2^{(1)}$-perfect crystal of level $l$, and then study the soliton cellular automaton constructed from it. The solitons of length $l$ are identified with elements of the $A_1^{(1)}$-crystal $\tilde{\mathcal{B}}_{3l}$. The scattering rule for our soliton cellular automaton is identified with the combinatorial $R$ matrix for $A_1^{(1)}$-crystals

Integrable Models From Twisted Half Loop Algebras

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaudin magnets, and Calogero-type models of particles on several half-lines meeting at a point.Comment: 22 pages, 1 figure, Introduction improved, References adde

Yangians, Integrable Quantum Systems and Dorey's rule

We study tensor products of fundamental representations of Yangians and show that the fundamental quotients of such tensor products are given by Dorey's rule.Comment: We have made corrections to the results for the Yangians associated to the non--simply laced algebra