On higher spin Uq(sl2)-invariant R-matrices
Andrei Bytsko
Abstract
The spectral decomposition of regular Uq(sl2)-invariant solutions of the Yang-Baxter equation is studied. An algorithm for finding all possible solutions of spin s is developed. It also allows to reconstruct the R-matrix from a given nearest neighbour spin chain Hamiltonian. The algorithm is based on reduction of the Yang-Baxter equation to certain subspaces. As an application, the complete list of inequivalent regular Uq(sl2)-invariant R-matrices is obtained for generic q and spins up to s=3/2. Some further results about spectral decompositions for higher spins are also obtained. In particular, it is proved that certain types of regular sl2-invariant R-matrices have no Uq(sl2)-invariant counterparts.
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