SMS scnews item created by Anthony Henderson at Mon 20 Oct 2008 1243
Type: Seminar
Distribution: World
Expiry: 31 Oct 2008
Calendar1: 31 Oct 2008 1205-1255
CalLoc1: Carslaw 159
CalTitle1: Algebra Seminar: Taylor -- The structure of finite unitary reflection groups

Algebra Seminar

The structure of finite unitary reflection groups

Don Taylor

31st October, 12:05-12:55pm, Carslaw 159


Given a finite dimensional Hilbert space V, a (complex or unitary) reflection is a linear transformation of V, of finite order, which fixes a hyperplane pointwise.

In 1954 Shephard and Todd obtained the complete classification of finite groups generated by reflections. For the primitive groups they relied on the classification of finite groups generated by homologies, which was achieved by Blichfeldt, Mitchell, and others, 50 years before.

In this talk I will outline a proof of this theorem based on the classification of embeddings between line systems, where a line system in V is a set of one-dimensional subspaces of V with prescribed angles between lines. This approach leads to the identification of the reflection groups as linear groups over finite fields.

After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

Anthony Henderson

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