#16087: Limit roots in the geometric representation of Coxeter groups
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Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: group theory | Resolution:
Keywords: days57, plot, coxeter | Merged in:
Authors: Jean-Philippe Labbé, Vivien | Reviewers:
Ripoll | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by jipilab):
Dear Travis,
Yes! that would be great to have a look at what is already available!
Is the hyperbolic Cartan type you mean the one of Bourbaki, Chein'69
(given in Humphreys). Where there are the compact and finite-volume
fundamental chambers?
We focus more on the general implementation of Coxeter groups where it is
possible to choose different values for the label "oo" for the bilinear
form giving "generalized" Coxeter graphs, so no conflict in sight a
priori. A classification of Lorentzian/Hyperbolic Cartan types is good to
have too!
You may have a look at http://arxiv.org/abs/1310.8608, where the
generalized Coxeter graphs of "level 2" are classified. These Coxeter
groups act on Lorentzian/hyperbolic space too. In this definition, "level
1" correspond to the union of finite-volume and compact hyperbolic Coxeter
groups.
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Ticket URL: <http://trac.sagemath.org/ticket/16087#comment:5>
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