Re: complex orthogonal group

From: Timothy Murphy <tim@xxxxxxxxxxxxxxxxxxxxxx>
Date: 22 Oct 2005 08:45:00 -0400

Tobias Fritz wrote:

> Is SO(n,C) generated by reflections (at non-null vectors)? Any hints or
> references would be appreciated!

There is a book by Coxeter on Complex Reflection Groups.
I don't have it with me, and don't recall clearly what he does,
except that he extends his method for representing
discrete reflection groups by Coxeter diagrams.

That allows me to bring up a question I have long wondered about.
What is the historical relation between Coxeter and Dynkin
regarding these diagrams?
I know Dynkin's usage is slightly more general;
but did he explicitly base his notation on Coxeter's?
It seems unlikely that both would come up with
exactly the same notation.

--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
.

Follow-Ups:
- Re: complex orthogonal group
  - From: Christopher J. Henrich
- Re: complex orthogonal group
  - From: Timothy Murphy

References:
- complex orthogonal group
  - From: Tobias Fritz

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