Seminar

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A deep connection between critical integrable statisical-mechanical models and fusion categories predates the discovery of the latter; the earlier formulations involved algebras such as that of Temperley and Lieb. The process of obtaining an integrable lattice model from categorical data was named "Baxterization'' by Vaughan J. However, the method is rather ad hoc; there is no way of telling a priori whether a given object in a given category will yield a solution of the Yang-Baxter equation needed for integrability. Moreover, finding solutions of Yang-Baxter can be a rather nasty procedure. I will discuss a much simpler linear equation for local weights of a lattice model defined by a (braided) fusion category whose solution yields conserved currents. All known solutions also solve the much-more complicated Yang-Baxter equation, and so Baxterise the category in a much simpler fashion. I find a general closed-form solution for categories with some simplifying properties, at least hinting that there may be an analogous solution in general.

Integrability from Categories?