**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 \(H\).