#9290: Implement Coxeter groups in their geometric representation
------------------------------------+---------------------------------
Reporter: nthiery | Owner: sage-combinat
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-5.13
Component: combinatorics | Resolution:
Keywords: coxeter | Merged in:
Authors: Travis Scrimshaw | Reviewers: Frédéric Chapoton
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15204 | Stopgaps:
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Changes (by tscrim):
* status: needs_review => positive_review
* reviewer: => Frédéric Chapoton
Old description:
> The root system / coxeter group code is designed from the ground up to
> allow for this extension.
>
> Steps:
>
> - Double check {{{CartanType(["H",3]).coxeter_diagram()}}} and friends
>
> - Given a coxeter diagram, construct the dynkin diagram {{{g}}}
> corresponding to the geometric representation; most of the time,
> this will involve roots of unity, and require e.g. a cyclotomic
> field (see also #8327)
>
> - Make sure that {{{L = RootSystem(g).root_space()}}} accepts such a
> diagram
>
> - Make sure that {{{WeylGroup(L)}}} accepts such a root space
>
> - Fix all the interfaces to properly reflect the generalization
> (e.g. WeylGroup above should really be CoxeterGroup).
New description:
The root system / coxeter group code is designed from the ground up to
allow for this extension.
Steps:
- Double check {{{CartanType(["H",3]).coxeter_diagram()}}} and friends
- Given a coxeter diagram, construct the dynkin diagram {{{g}}}
corresponding to the geometric representation; most of the time,
this will involve roots of unity, and require e.g. a cyclotomic
field (see also #8327)
- Make sure that {{{L = RootSystem(g).root_space()}}} accepts such a
diagram
- Make sure that {{{WeylGroup(L)}}} accepts such a root space
- Fix all the interfaces to properly reflect the generalization
(e.g. WeylGroup above should really be CoxeterGroup).
Apply:
* [attachment:trac_9290-geometric_coxeter_groups-ts.patch]
* [attachment:trac-9290-review.patch]
--
Comment:
Hey Frederic,
I can't see an easy way to do so either. There might be a solution, but
it'll probably be either complicated or cumbersome.
Thanks for doing the review,[[BR]]
Travis
--
Ticket URL: <http://trac.sagemath.org/ticket/9290#comment:18>
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