Integrable lattice models, discrete holomorphicity and quantum group symmetries
by Michael Wheeler
Abstract: This talk will give an introduction to dense and dilute Temperley-Lieb loop models, and review what is meant by a discretely holomorphic observable in such models. We show that these observables can be recovered naturally in the language of currents built from quantum group generators, and that discrete holomorphicity is actually a consequence of current conservation. Along the way, we will rely on the connection of the loop models with vertex models based on evaluation representations of the underlying quantum groups.
This is joint work with Yacine Ikhlef, Robert Weston and Paul Zinn-Justin.