Dimer representations of the Temperley–Lieb algebra

A new spin-chain representation of the Temperley–Lieb algebra TLn(β=0)TLn(β=0) is introduced and related to the dimer model. Unlike the usual XXZ spin-chain representations of dimension 2n2n, this dimer representation is of dimension 2n−12n−1. A detailed analysis of its structure is presented and found to yield indecomposable zigzag modules.