SEMINAR: Groups and Combinatorics Seminar: Reflection subgroups of unitary reflection groups

Time and place: 16:00 Friday 19 August in Weatherburn LT

Speaker: Don Taylor (The University of Sydney)

Title: Reflection subgroups of unitary reflection groups

Abstract: The usual notion of a reflection in Euclidean space has a natural analogue in vector spaces over the complex numbers. In this talk I will give a brief introduction to finite groups generated by complex (i.e., unitary) reflections and report on some results characterising reflection subgroups and their normalisers. An imprimitive unitary reflection group is a normal subgroup of the group of m-th roots of unity by a symmetric group. For these groups there are uniform methods of proof. However, for 15 exceptional (primitive) groups I resort to calculations using the Magma computation algebra system.