Godsil, Chris; matematični kolokvij september 2001

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Braid Groups and Association Schemes

Chris Godsil

Univerza Waterloo, Kanada

27. september 2001

In 1989, Vaughan Jones introduced a class of objects called spin models. He showed that each spin model gave rise to a link invariant, using ideas from Statistical Mechanics (in particular, partition functions). He also showed that each spin model gives rise to a special type of representation of the braid group, and that this lead to another construction of the same link invariants. It is extremely surprising that both approaches have close interactions with important topics in Combinatorics. In the first case, the connection is with Tutte polynomials---an important class of polynomials related to the chromatic polynomial of a graph. In the second case, we are lead to association schemes, which are algebraic objects associated with highly regular combinatorial structures. In my talk I will decribe these connections, and discuss some of the questions they raise.