# Algebra Seminar

### Complex reflection groups.

Friday 6th November, 12-1pm, Carslaw 273.

Let G be a finite complex reflection group, acting on V = Cn. Fix a primitive root of unity zeta and for g\in G denote by V(g,zeta) the eigenspace of g in V for the eigenvalue zeta. Choose g such that this eigenspace E has maximum possible dimension and let N be the normaliser of E in G. Then the restriction of N to E defines a complex reflection group in E, uniquely determined up to linear isomorphism by the order d of zeta; call it G(d). In the talk various properties of the 'satellites' G(d) of G will be discussed.