[GAP Forum] Stabilizer of a vector for Coxeter Groups

[Alexander Hulpke]

Dear GAP-Forum,

>
Vincent Chaudrelier wrote:

> I've tried with F4 by defining it as a matrix group then typing
> something like "Stabilizer(F4,[[1],[0],[0],[0]]);" 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  
> not
> 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.

Best,

    Alexander Hulpke