
School of Mathematics and Statistics
Tony Springer
Mathematical Institute, Utrecht
Complex reflection groups.
Friday 6th November, 121pm, Carslaw 273.
Let G be a finite complex reflection group, acting on
V = C^{n}. 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.
