INTEGRABLE SPIN CHAINS AND REPRESENTATION THEORY

A series of integrable spin chains related to special tensor product representations of Temperley - Lieb algebra is constructed. The generator of the TL-algebra is a rank one projector acting on ℂⁿ ⊗ ℂⁿ. The spectra of these spin chains with appropriate boundary conditions are the same and equivalent to the spin 1/2 XXZ-model while the multiplicities of the eigenvalues are different and depend on n. The generators of the TL-algebra with rankX_j bigger than 1 are also mentioned.