#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:38 tscrim]:
> In many ways, we are beating a dead horse as you have basically done
what I am asking for already (with the specializing being done in the
different implementations of a Coxeter group).
Well, let's keep it as it is for now then.
> Then let's leave those tests in. That is the only thing I am asking for
here.
Fine.
> I am pretty sure it appears in a stable release (i.e., 7.1), so yes.
After Nicolas' comment that {{{WeylGroup}}} uses {{{.action}}}, I moved it
back to {{{action*}}}...
> my interpretation of Christian's first comment was this was a property
of the realization of the group, not of the group itself. So the group's
`is_crystallographic` should just call that of its Coxeter type/matrix.
Yes, for real groups I only wanted the `is_crystallographic` of the group
to call the one of the Coxeter type/matrix. But complex reflection groups
can still be crystallographic (though they only are if they are real and
crystallographic), so they deserve the method {{{is_crystallographic}}}
without having a Coxeter type/Coxeter matrix attached to them.
> So I see no ambiguity, and in fact, I think the Weyl groups are very
explicit about this.
But what if {{{w}}} is an element of the group and {{{v}}} is a *Sage
vector*. Does it represent an element in the vector space spanned the
simple roots, or by the simple coroots, or by the fundamental weights, or
by the fundamental coweights? Or does that not matter since the actions
are all the same?
--
Ticket URL: <http://trac.sagemath.org/ticket/20402#comment:42>
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