Constructing representations of Hecke algebras for complex reflection groups

Understand

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups.

• We first describe computational methods for the construction of irreducible representations of these algebras, including a generalization of the concept of $W$-graph to the situation of complex reflection groups.
• We then use these techniques to find models for all irreducible representations in the case of complex reflection groups of dimension at most three.
• Using these models we are able to verify some important conjectures on the structure of Hecke algebras.