Discrete holomorphicity and quantized affine algebras
Paul Zinn-Justin, LPTHE
This is joint work with I. Ikhlef, R. Weston and M. Wheeler. I will discuss the interplay between two properties of two-dimensional statistical models, namely integrability (or exact solvability) and discrete holomorphicity. After introducing these concepts, I will explain how the Bernard-Felder construction of nonlocal currents out of quantized affine algebras provides a link between them, relating the discrete holomorphicity equation with conservation of these nonlocal currents. I will discuss as an example the case of the Temperley–Lieb (dense) loop model.