#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:35 nthiery]:
> Oh, I had not noticed that `CoxeterMatrixGroup` were acting on plain
vectors with '*'.
Yes, the elements are matrices which act on vectors :-)
> As you mention this is very ambiguous. For a Weyl group this is even
worst: is the vector interpreted as in the span of the (co)roots? of the
(co)weights? in the ambient space?
I agree.
> For now, I'd rather keep the notations as explicit as possible (in
particular, it's easier to document a method `.action` than an overloaded
operator). And leave us room in the future to overload '*', either by
default, or upon explicit request from the user.
One could define `_act_on_` in different ways for elements in the
root/coroot/weight/coweight space, and not at all for plain vectors. But
on the reflection group side there is no class for elements in {{{V}}} and
in {{{V^*}}} yet. I am okay with both: considering the action on vectors
for now on elements in {{{V}}}, or removing the coercion for now.
--
Ticket URL: <http://trac.sagemath.org/ticket/20402#comment:36>
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