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Dimer representations of the Temperley-Lieb algebra

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

preprint2014arXivOpen access
Alexi Morin-DuchesneJorgen RasmussenPhilippe Ruelle
cond-mat.stat-mechmath-phmath.MPhep-th
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Alexi Morin-DuchesneJorgen RasmussenPhilippe Ruelle

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