SMS scnews item created by Anthony Henderson at Wed 3 Dec 2008 1305
Type: Seminar
Distribution: World
Expiry: 5 Dec 2008
Calendar1: 5 Dec 2008 1205-1255
CalLoc1: Carslaw 373
CalTitle1: Algebra Seminar: Michel -- Automorphisms of complex reflection groups
Auth: anthonyh@bari.maths.usyd.edu.au

Algebra Seminar

Automorphisms of complex reflection groups

Jean Michel

5th December, 12:05-12:55pm, Carslaw 373 ***NOTE UNUSUAL ROOM***


Abstract

I report on joint work with Ivan Marin. We prove that any automorphism of an irreducible finite complex reflection group is, apart from the single exception of the symmetric group on six letters, the product of automorphisms of 3 kinds:
  • a 'diagram' automorphism, induced by the ambient linear group;
  • a central automorphism;
  • a 'Galois' automorphism, a new kind of automorphisms which come from an embedding of the Galois group of the defining field into the outer automorphism group using Galois cohomology properties of the reflection representation.
We then extend the result to a large class of non-irreducible groups using an extension of the Krull-Remak-Schmidt theorem.

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 anthonyh@maths.usyd.edu.au.