Dimer representations of the Temperley-Lieb algebra

Abstract

A new spin-chain representation of the Temperley-Lieb algebra $T{L}_n(\beta =0)$ 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.

23 pages. Comments and references added

References in corpus (4)

• Associative-algebraic approach to logarithmic conformal field theories
• An introduction to the dimer model
• Fusion Algebras of Logarithmic Minimal Models
• Transfer matrix for spanning trees, webs and colored forests

Cited by in corpus (1)

• Multipoint correlators in the Abelian sandpile model