#16087: Limit roots in the geometric representation of Coxeter groups
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Reporter: nthiery | Owner:
Type: | Status: new
enhancement | Milestone: sage-6.2
Priority: major | Keywords: days57, plot
Component: group | Authors: Jean-Philippe Labbé, Vivien
theory | Ripoll
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
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Related tickets:
- [ ] http://trac.sagemath.org/ticket/9290
- [ ] http://trac.sagemath.org/ticket/13248
TODO:
- Cleanup this description!!!!!
Matrix representation for Coxeter groups
- [ ] Root space for general Coxeter groups
sage: L = RootSystem(<"generalized" coxeter matrix>).root_space()
sage: W = L.reflection_group() returns an instance of
"CoxeterMatrixGroup"
- [ ] Generalize CoxeterMatrixGroup from WeylGroup
http://trac.sagemath.org/ticket/15703
Make it full featured
- [ ] Add a category for Lorenzian/HyperbolicCoxeterGroups
Inside the hierarchy:
CoxeterGroups
FiniteCoxeterGroups
WeylGroups
Lorenzian/HyperbolicCoxeterGroups: generic methods for Coxeter
groups in an appropriate matrix representation
- [ ] Allow <-1 coefficients in the Coxeter diagram
- [ ] positive roots by depth
- [X] Missing: elements of the group as matrices: for free from the
above
- [X] fundamental weights in the root space
- [X] finding all reduced words
- [ ] signature of the bilinear form
- [ ] parabolic elements / elliptic elements of the group
algo: build all elements, and select those by a criterion
of diagonalizability and max modulus of the eigenvalues
- [ ] Compute limit roots L.limit_roots(...)
- [ ] Visualize limit roots L.plot_limit_roots()
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Ticket URL: <http://trac.sagemath.org/ticket/16087>
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