[GAP Forum] Stabilizer of a vector for Coxeter Groups

[Caudrelier, Vincent]

All,

 

I'm trying to compute the stabilizer of a given vector in the underlying
essential vector space of a finite Coxeter group seen as a reflection
group acting on this vector space.

 

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.

 

I hope my question makes enough sense and that someone can help me.

 

Many thanks

 

------------------------
Dr Vincent CAUDRELIER
Lecturer in Mathematics
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City University
Centre for Mathematical Science
Northampton Square
LONDON EC1V 0HB
UK
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tel: +44 (0) 2070 408498