Revision history [back]

This automorphism is realized by conjugation with the longest element in $W$:

sage: W = CoxeterGroup(['A',3],implementation="reflection")
sage: S = W.simple_reflections()
sage: Sauto = { i: W.w0*S[i]*W.w0 for i in S.keys() }
sage: S
Finite family {1: [-1  1  0]
[ 0  1  0]
[ 0  0  1], 2: [ 1  0  0]
[ 1 -1  1]
[ 0  0  1], 3: [ 1  0  0]
[ 0  1  0]
[ 0  1 -1]}
sage: Sauto
{1: [ 1  0  0]
 [ 0  1  0]
 [ 0  1 -1], 2: [ 1  0  0]
 [ 1 -1  1]
 [ 0  0  1], 3: [-1  1  0]
 [ 0  1  0]
 [ 0  0  1]}