Vertex Models
by
V.S. Sunder
The Institute of Mathematical Sciences, Madras, India

This talk will describe `vertex models' in the sense of Vaughan Jones. These are very special, seemingly simple `commuting squares'. After defining these objects, we shall proceed to the description, via the so-called Jones diagrams, of the tower of higher relative commutants of the subfactor constructed out of the given vertex model. (This description also shows the reason for the use of this `statistical mechanical' expression in this context.) Finally, we shall discuss the simplest examples of these vertex models and what the above-mentioned tower looks like in these cases.

Date received: March 4, 1999