Tuesday, November 7, 14:00, 7.527.
Alexandre Esterle (Amiens)
Bilinear forms for self-dual W-graphs.
W-graphs were first introduced by Kazhdan and Lusztig in 1979. In their
paper, they showed how to construct W-graphs affording irreducible
representations in type A. Their method generalizes to many types and in
1981, Gyoja proved that any irreducible representation of an Iwahori-Hecke
algebra could be afforded by a W-graph.
In this talk, we will explain how W-graphs give us representations of Hecke
algebras and then explain representation properties which can be deduced from
those W-graphs. In particular, the dual representation of a representation
afforded by a W-graph is afforded by a W-graph which can be determined in a
combinatoric way. We will look at properties which should naturally be
verified by W-graphs affording self-dual representations and see they are not
always verified. We will then show how to find W-graphs verifying those
properties for a given self-dual representation.
We will then use those properties to look at the image of Artin as subgroups
of the invertible elements of Hecke algebras in type H4.