Changes between Initial Version and Version 4 of Ticket #15272


Ignore:
Timestamp:
03/18/14 17:51:14 (8 years ago)
Author:
vittucek
Comment:

New commits:

7bb7c3bDecorate ClassicalWeylSubgroup.simple_reflections() with @cached_method.
6db7b6dFirst version of minimal coset representatives.
472c090Add parabolic minimal_coset_representatives, bruhat_graph and bruhat_poset

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  • Ticket #15272

    • Property Status changed from new to needs_review
    • Property Authors changed from to Vít Tuček
    • Property Cc nthiery bump added
    • Property Summary changed from Bruhat posets and Bruhat graphs for parabolic subgroups to Bruhat posets and Bruhat graphs for parabolic subgroups of finite Weyl groups
    • Property Branch changed from to u/vittucek/ticket/15272
    • Property Milestone changed from sage-6.1 to sage-6.2
    • Property Commit changed from to 472c0908fba197fe9bb73742caab1ebfcde27b53
  • Ticket #15272 – Description

    initial v4  
    1 This patch extends the functionality of bruhat_poset and introduces new parabolic_bruhat_graph for finite Weyl groups.
     1This patch adds method minimal_representatives and extends the functionality of bruhat_poset and bruhat_graphs.
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    33Let 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.
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    5 This patch adds a parameters index_set (= S) and side (left / right).
    6 
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    8 ----
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    11 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
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    13 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.
     5This patch adds a parameters index_set (= S), crossed_nodes and side (left / right).