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Dimer representations of the Temperley-Lieb algebra (1409.3416v2)
Published 11 Sep 2014 in math-ph, cond-mat.stat-mech, hep-th, and math.MP
Abstract: A new spin-chain representation of the Temperley-Lieb algebra $TL_n(\beta=0)$ is introduced and related to the dimer model. Unlike the usual XXZ spin-chain representations of dimension $2n$, this dimer representation is of dimension $2{n-1}$. A detailed analysis of its structure is presented and found to yield indecomposable zigzag modules.