Talk:Coxeter group

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Mathematics rating:	B Class	High Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 22:56, 16 June 2007 (UTC)

Possible improvements:

• Describe dihedral groups explicitly as finite Coxeter groups in the Euclidean plane, and explain the geometric meaning of the relator.
• Describe the way in which the symmetric group S_n acts by reflections in Euclidean n-space.
• State the theorem on special subgroups: each subset of the generators generates a subgroup isomorphic to a Coxeter group.
• Say the exact manner in which the group acts by affine reflections: the "geometric representation".
• Give the exact list of which Coxeter groups act discretely by isometric reflections in Euclidean space of some dimension. This list is not too much more complicated than the list of finite Coxeter groups.
• Explain how some Coxeter groups (such as certain triangle groups) act discretely in hyperbolic space of some dimension, generated by isometric reflections.

--Mosher 10:48, 8 October 2005 (UTC)

[edit] Update notice

Does anyone watching have an interest in this page? I've expanded an article Coxeter-Dynkin diagram, using Coxeter groups, but a different letters than shown here - used in his book Regular polytopes. Looks like diagrams here are the original letters which Coxeter renamed a bit to A-G for finite groups, and P-W for infinite groups.

I'd like to update this article to reflect this different system. I'm happy to make a conversion table showing the old/new systems. I'd like all the uniform polytope articles to reference Coxeter group and the group name.

I'll hold for a week for responses. Thanks! Tom Ruen 04:50, 25 January 2007 (UTC)

Please do not make those changes here. The terminology on the other page has some serious mistakes and does not align itself with how most of the mathematics community views Dynkin diagrams and Coxeter graphs. I will address my problems with the other page when I have sufficient time.

[edit] Rank

The rank of a Coxeter group is not defined. —Preceding unsigned comment added by 81.210.238.84 (talk) 08:03, 15 April 2008 (UTC)