#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 tscrim):
Hey Jean-Philippe,
Not quite. A hyperbolic Cartan type is an indefinite type, which when you
remove any node, you get an affine or finite Cartan type (and compact
means they are all finite type). This is the Cartan type version analogous
statement to Prop 6.8 from Humphreys.
From this, there are only a finite number of rank 3 types, and nothing
with would generate a label of 5 in the corresponding Coxter graph. So the
Coexter graphs from these Cartan types would span a large subclass of the
hyperbolic, but would not include all hyperbolic Coxeter diagrams (akin to
the finite type).
It might be worthwhile (mathematically) to look at level k Cartan types
too.
So we're doing different things, but with some potential overlap. I want
to try and mitigate conflicts and duplication (if there would be any).
I've posted my current WIP in case there's anything you want to pull from
that, and any comments/suggestions you have are useful too. Be warned,
it's somewhat of a mess still.
--
Ticket URL: <http://trac.sagemath.org/ticket/16087#comment:6>
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