Analytical Bethe Ansatz for quantum-algebra-invariant spin chains

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz (BA) method. In particular, we determine in this way the spectrum of the transfer matrices of the U_q[su(2)]-invariant spin chains associated with A₁⁽¹⁾ and A₂⁽²⁾ in the fundamental representation. The quantum-algebra invariance of these models plays an essential role in obtaining these results. The BA equations for these open chains are "doubled" with respect to the BA equations for the corresponding closed chains.