#20402: Make subword complexes compatible with real reflection groups
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Reporter: stumpc5 | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.2
Component: combinatorics | Resolution:
Keywords: reflection group, | Merged in:
coxeter group, subword complex, | Reviewers:
days80 | Work issues:
Authors: Christian Stump | Commit:
Report Upstream: N/A | 295d784db0ae24bed97ed7b4d3777df9dbd652c2
Branch: u/stumpc5/20402 | Stopgaps:
Dependencies: #11187 |
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Comment (by stumpc5):
Replying to [comment:33 nthiery]:
> Replying to [comment:31 stumpc5]:
> > I don't get your point of switching: what is wrong with having the
method `action` and then using this method in the body of `_act_on_`?
>
> Just that I am not sure that we want to overload/polute '*' with this;
and if we do, it should be done consistently for Weyl groups as well.
One reason in favour is that elements in {{{CoxeterGroup}}} are matrices,
so they use '*' anyways. Otherwise, I would have to re-enable the method
{{{action}}} there which is simply using '*'.
One reason against is that for complex reflection groups, the action on
the space and on its dual are different. And since both are represented by
vectors (in the dual bases {ei} and {xi}), the '*' does not see this for
now. But one could have an optional argument {{{in_dual}}} for
{{{action}}}.
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Ticket URL: <http://trac.sagemath.org/ticket/20402#comment:34>
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