NEW BOUNDARY-CONDITIONS FOR INTEGRABLE LATTICES

New boundary conditions for classical integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice, are presented. These integrable extensions are formulated in terms of a ge neric XXX Heisenberg magnet interacting with two additional spins at e ach end of the chain. The construction uses the most general rank-1 an satz for the 2 x 2 L-operator satisfying the reflection equation algeb ra with rational r-matrix. The associated quadratic algebra is shown t o be that of dynamical symmetry for the A(1) and BC2 Calogero-Moser pr oblems. Other physical realizations of our quadratic algebra are also considered.