A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra (Q2851179)

The authors study loop models on a lattice wrapped around a cylinder, where a section of the cylinder has \(N\) sites. For the geometry of the cylinder, the relevant algebra is the enlarged periodic Temperley-Lieb algebra \(\mathcal{E}\mathrm{PTL}_N(\beta,\alpha)\). Two representations of the enlarged periodic Temperley-Lieb algebra \(\mathcal{E}\mathrm{PTL}_N(\beta,\alpha)\) are studied in this paper: the link representation \(\omega_d\) for the loop models and the representation \(\tau\) for the XXZ spin chain. The main result of this paper is the construction of an interwinter between the representation \(\omega_d\) and the restriction of the representation \(\tau\).