**Speaker:** Alexandre Esterle (Amiens)

**Title:** *Bilinear Forms on Self-Dual W-Graphs*

**Abstract:**

W-graphs give us combinatorial models for any irreducible representation of an Iwahori-Hecke algebra. We will look at the properties which can be deduced directly from the graphs. In particular, given an irreducible representation associated to a W-graph, there is a way to define a W-graph affording the dual representation. We will consider properties which should be verified by W-graphs affording self-dual representations and define a bilinear form when those conditions are verified.