The Classical rr-Matrix for the Relativistic Ruijsenaars-Schneider System

We compute the classical $r$-matrix for the relativistic generalization of the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the speed-of-light parameter $\lambda$. We connect it with the non-relativistic Calogero-Moser $r$-matrix $(\lambda \rightarrow -1)$ and the $\lambda = 1$ sine-Gordon soliton limit.Comment: LaTeX file, no figures, 8 page

Parametrization of semi-dynamical quantum reflection algebra

We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by dynamical conjugation matrices, Drinfel'd twist representations and quantum non-dynamical $R$-matrices. They yield factorized forms for the monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on construction of Hamiltonian

Structures in BC_N Ruijsenaars-Schneider models

We construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket behavior, although the dynamical dependence is more complicated. Commuting Hamiltonians stemming from the BC_N Ruijsenaars-Schneider Lax matrix are shown to be linear combinations of particular Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings. Uniqueness of such commuting Hamiltonians is established once the first of them and the general analytic structure are given.Comment: 18 pages, gzip latex fil

Spin chains from dynamical quadratic algebras

We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously defined three general quadratic reflection-type algebras: respectively non-dynamical, semidynamical, fully dynamical.Comment: 12 pages, no figures; v2: corrected formulas of the last sectio

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

Reflection matrices from Hadamard-type Temperley-Lieb R-matrices

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