Colloquium
3:00 p.m., Friday (Jan. 18)
Math Annex 1100
David Wales
Cal Tech
Linearity of Artin groups of finite type
I will talk on joint work with Arjeh Cohen which
extends the recent work on linearity of the Braid
groups to Artin groups of finite type. A group is
called linear if there is a faithful finite dimensional
representation. It has only recently been shown by
Krammer and Bigelow that the Braid groups are linear.
We have been able to generalize many of the arguments
to the Artin groups of finite type, namely A_n, B_n, C_n,
D_n, G_2, F_4, E_6, E_7, and E_8. The Braid group is the
group A_n. This is done by recognizing many of the arguments
of Krammer as results on the root systems of the corresponding
type. Using these properties, we are able to produce an action
of the Artin group on a vector space which has as its basis
the positive roots. We are able to show it is faithful and
so the groups are linear.
