# Darstellungstheorietage and Nikolaus Conference 2013

Speaker: Johannes Hahn (Jena)

Title: Gyoja's $$W$$-Graph Algebra

Abstract: $$W$$-graphs are combinatorial objects that encode matrix representations of Hecke algebras. Their definition is explicit but does not offer much immediate insights. It is for example not at allt clear what graphs actually occur as $$W$$-graphs. Goyja proved that every isomorphy class of $$H$$-modules contains $$W$$-graphs and introduced an auxilliary algebra for this proof. A careful examination of this algebra leads (among other things) to new necceassry conditions for graphs to be $$W$$-graphs. A structural conjecture about the $$W$$-graph algebra leads to new insights into balanced and cellular representations of $$H$$.