Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices

Abstract

A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a representation ring equivalent to the representation ring of the sl_2 Lie algebra. This algebra U_q is the symmetry algebra of the corresponding open spin chain.Comment: 14 pages LaTex; typos corrected and two references adde