#11010: Implementation of the SubwordComplex as defined by Knutson and Miller
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Reporter: stumpc5 | Owner: tbd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: combinatorics | Resolution:
Keywords: subword complex, | Merged in:
simplicial complex | Reviewers:
Authors: Christian Stump | Work issues:
Report Upstream: N/A | Commit:
Branch: u/stumpc5/11010 | 6b65d7003f98adc0aab9984cfec28de9b6311eab
Dependencies: | Stopgaps:
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Comment (by stumpc5):
First, the definition of subword complexes is for Coxeter groups (finite
or infinite), but many of its properties (see my paper with Vincent
referenced in the header) come from understanding roots and weights.
Second, I think the current failure is only because the method
{{{WeylGroup.roots}}} is missing, as is the method
{{{WeylGroupElement.action_on_root_indices}}}.
* Do you know how I can get the list of (simple, positive, almost
positive, all) roots of a root system when I only have the Weyl group
{{{W}}} at hand? It seems that I have to build a root system from the
Cartan type, though it seems more natural to have a method
{{{WeylGroup.root_system}}} or at least {{{WeylGroup.cartan_matrix}}},
wouldn't it?
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Ticket URL: <http://trac.sagemath.org/ticket/11010#comment:56>
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