76.7 Reflections

Reflections( W )

returns the set of reflections in the Coxeter group W (as permutations). The i-th entry in this list is the reflection along the i-th root in W.roots.

    gap> W := CoxeterGroup( "B", 2 );; W.roots;
    [ [ 1, 0 ], [ 0, 1 ], [ 1, 1 ], [ 2, 1 ], [ -1, 0 ], [ 0, -1 ],
      [ -1, -1 ], [ -2, -1 ] ]
    gap> Reflections( W );
    [ (1,5)(2,4)(6,8), (1,3)(2,6)(5,7), (2,8)(3,7)(4,6), (1,7)(3,5)(4,8), 
      (1,5)(2,4)(6,8), (1,3)(2,6)(5,7), (2,8)(3,7)(4,6), (1,7)(3,5)(4,8) ]

This function requires the package "chevie" (see RequirePackage).

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