Stabilisers of eigenvectors in complex reflection groups

Presented by: Sinead Wilson, UQ

Complex reflection groups are finite subgroups of unitary groups which are generated by complex reflections. They are a generalisation of real reflection groups. The invariant theory of irreducible real reflection groups is encoded in the eigenvalues of certain elements, called Coxeter elements, and conversely, Kostant showed (in the case of Weyl groups) that Coxeter elements are characterised by a certain property of their eigenvalues. Kostant's result was refined by Kamgarpour, who gives a more precise relation between the eigenvalues of any element and the stabilisers of the corresponding eigenvectors. In this talk, we discuss a generalisation of Kamgarpour's result to complex reflection groups.