In the field of exactly solvable models of 2d Statistical Mechanics, the Temperley-Lieb algebra is the underlying structure for various classes of lattice models, such as the Ising, O(n), percolation, six-vertex, Solid-on-Solid models, etc. In this talk, I focus on the affine Temperley-Lieb (ATL) algebra, which is relevant to spatially periodic systems and/or bulk correlations in these lattice models. I will review the essential results form the seminal work of Graham and Lehrer (1998) on the representation theory of the ATL algebra, and more recent studies on the subject. Then, I will present a collection of new results on the construction of a tensor (or fusion) product for the modules over the ATL algebra, and the calculation of fusion rules, which share some common features with the fusion of Virasoro modules in Conformal Field Theory in the scaling limit..

https://indico.math.cnrs.fr/event/16187/