#15272: Bruhat posets and Bruhat graphs for parabolic subgroups
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Reporter: vittucek | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.13
Component: combinatorics | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This patch extends the functionality of bruhat_poset and introduces new
parabolic_bruhat_graph for finite Weyl groups.
Let W be a finite Weyl group and let W_S be the subgroup of W generated by
reflections associated with a subset S of simple roots. Then the cosets W
/ W_S have unique representatives of minimal length which are ordered by
the Bruhat order of W. Similarly for W_S \ W. These poset structures
appear in many places, e.g. intersection cohomology of generalized flag
varieties or nilpotent Lie algebra cohomology.
This patch adds a parameters index_set (= S) and side (left / right).
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Introducing parabolic_bruhat_graph is ugly. Ideally, one would just extend
the existing bruhat_graph. However, this method is based upon
bruhat_interval which belongs to categories/coxeter_groups.py
I was unsure where to put the code, which I haven't written yet nor which
I need in the foreseeable future anyway. Since it seems that the best
course of action would be to implement class (or category?) for parabolic
subroot systems / groups I think that one more method for Weyl group is
not much of an issue.
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Ticket URL: <http://trac.sagemath.org/ticket/15272>
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