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.

14 pages LaTex; typos corrected and two references added

References in corpus (2)

• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Asymmetric Twin Representation: the Transfer Matrix Symmetry

Cited by in corpus (1)

• Murphy elements from the double-row transfer matrix