ADE graphs and associated lattices, weights and quarks

Abstract:

A general connected simple graph X supports a rich metrical geometry, fascinating combinatorics and tight connections with reflection/Coxeter group theory. This can all be laid out in an elementary fashion with the Mutation Game, and the ADE graphs and their affine variants figure prominently. 

In this lecture we introduce the dual Numbers Game due to Moses and also studied by Eriksson, which involve weights as opposed to roots. We will naturally be led to novel views of important lattices, and in the seemingly simple case of A2 we meet the eight-fold way of particle physics which is a mainstay of the modern understanding of quarks and their relations with other elementary particles.

This lecture will be one of several in a series roughly on ADE graphs, but will be largely self-contained.