Opened 9 years ago
Last modified 5 years ago
#16087 new enhancement
Limit roots in the geometric representation of Coxeter groups — at Version 3
Reported by: | Nicolas M. Thiéry | Owned by: | |
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Priority: | major | Milestone: | sage-6.4 |
Component: | group theory | Keywords: | days57, plot, coxeter, days64 |
Cc: | Sage Combinat CC user, Jean-Philippe Labbé, Vivien Ripoll, Travis Scrimshaw | Merged in: | |
Authors: | Jean-Philippe Labbé, Vivien Ripoll | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Related tickets:
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()
Change History (3)
comment:1 Changed 9 years ago by
Cc: | Vivien Ripoll added |
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comment:2 Changed 9 years ago by
Keywords: | coxeter added |
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comment:3 Changed 9 years ago by
Description: | modified (diff) |
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