The canonical representation works by defining the basis vectors to have whatever inner products you want them to have in order to satisfy the Coxeter relationships you're given. You end up with a vector space and a metric, but the metric is presumably not going to have any nice properties. --Michael On Wed, Nov 28, 2012 at 2:05 PM, Mike Stay <metaweta@gmail.com> wrote:
On Wed, Nov 28, 2012 at 10:54 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Are you seeking a representation by finite matrices over the reals? How do you know that a representation of the desired type exists?
I don't. There's something about a "canonical linear representation" in the Wikipedia article
http://en.wikipedia.org/wiki/Coxeter_complex#The_canonical_linear_representa... that suggests to me that such a thing is possible, but I don't quite understand it yet. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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