#20477: reduced words in complex reflection group
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Reporter: stumpc5 | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.2
Component: combinatorics | Resolution:
Keywords: complex reflection groups, | Merged in:
reduced words | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by stumpc5):
* cc: jmichel (added)
Comment:
Replying to [comment:3 nthiery]:
> Just wondering: is that still the case for a complex reflection group W
that, if you take a parabolic subgroup `W_I` and its coset representatives
`W^I` the factorization of an element `w=w_I w^I` is reduced?
> (that is `len(w)=len(w_I)+len(w^I)`)?
Complex reflection groups behave *very differently* with respect to a
simple system (which basically doesn't exist, at least not in a Coxeter
combinatorial sense). I believe this does not work, but Jean can certainly
say what is possible and what is not.
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Ticket URL: <http://trac.sagemath.org/ticket/20477#comment:4>
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