Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models
Mon, Jun. 21st 2021, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
In the dense O(n) loop model, the scaling properties of the random curves are encoded in the correlators of connectivity operators. Each such operator is naturally associated to a standard module of the periodic Temperley-Lieb algebra. We introduce a new family of representations of this algebra, with connectivity states that have two marked points, and argue that they define the fusion of two standard modules. We obtain their decomposition on the standard modules for generic values of the parameters, which in turn yields the structure of the operator product expansion of connectivity operators.