Bratteli diagrams, locally semisimple algebras: de Finetti's theorem, Young graph, ramdom walks on graded graphs

I plan to describe the link between Bratteli diagrams (N-graded graphs) and characters of the corresponding algebras. We start from the classical example: a reformulation of de Finetti's theorem for Pascal triangle. Then we describe Young graph for symmetric group and similar graphs for the Brauer algebras and infinite symmetric semigroup. Two last examples lead to two natural random walks on these graphs (current research on this topic is a part of ERC project IChaos). I plan to make the talk clear for the 2nd-3rd year students. First of all, I will remind shortly the necessary facts from the representation theory of finite groups (in particular, symmetric groups).