Maths HEP Lunchtime Seminars: How the 8-Vertex Model got its Tail
4 June 2004 00:00 in CM221
"In the high and far-off times the 8-vertex model was unassailable, for its charge was unconserved. But through the skill of Baxter was it brought low and humbled. Three mighty weapons did he use - the Q operator - the trick of inversion - and the `intertwiner'. This victory bore many fruits - quantum inverse scattering was among them. The seed did cover all the world and gave birth to quantum groups. While Baxter rose to glory, his tools lay forgotten, abandoned by those corrupted by algebra. But a new age has dawned. The tools are reforged and shine bright in a crystalline algebraic light. In this account I shall discuss the intertwiner - a poor name for a thing of beauty. I shall describe its role in producing new and exact expressions for correlation functions of the 8-vertex model and its fusion brethren, and will show how a key object, the tail operator, is constructed in terms of it. I will opine on how the intertwiner may be related to the twist of Drinfeld. I will draw lots of pictures."