[GAP Forum] Stabilizer of a vector for Coxeter Groups
hulpke at mac.com
Tue May 20 18:19:42 BST 2008
Vincent Chaudrelier wrote:
> I've tried with F4 by defining it as a matrix group then typing
> something like "Stabilizer(F4,[,,,]);" but I suspect
> this is
> not doing what I want but rather it gives the stability group of the
> group element corresponding to the reflection associated to e_1 and
> the stability group of e_1 itself.
GAP acts consistently from the right, i.e. matrix groups act on row
vectors. What you give as object to be stabilized looks like a matrix
with one column, this is not a well-defined action.
Stabilizer(F4,[1,0,0,0]) should give the desired result.
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