|Dept.||University of Minnesota|
For a Coxeter group W, a W-graph is a graph which produces a nice basis of the corresponding representation of W and also describes the action of W on the basis elements. Even when W is finite and its irreducible characters are known, W-graphs are still useful for understanding representations of W. In this talk, I will talk about W-graphs when W is an (extended) affine symmetric group, especially when these graphs are associated with “two-row partitions”. Also I will discuss the connection between them and Lusztig’s periodic W-graph. This work is joint with Pavlo Pylyavskyy.