82.1 HeckeReflectionRepresentation

HeckeReflectionRepresentation( W )

returns a list of matrices which give the reflection representation of the Iwahori-Hecke algebra corresponding to the Coxeter group W. The function Hecke must have been applied to the record W.

    gap> v:= X( Rationals );;  v.name := "v";;
    gap> H := Hecke(CoxeterGroup( "B", 2) , v^2, v);
    Hecke(CoxeterGroup("B", 2),[ v^2, v^2 ],[ v, v ])
    gap> ref:= HeckeReflectionRepresentation( H );
    [ [ [ -v^0, 0*v^0 ], [ -v^2, v^2 ] ], 
      [ [ v^2, -2*v^0 ], [ 0*v^0, -v^0 ] ] ] 

    gap> H := Hecke( CoxeterGroup( "H", 3 ));;  
    gap> HeckeReflectionRepresentation( H );
    [ [ [ -1, 0, 0 ], [ -1, 1, 0 ], [ 0, 0, 1 ] ], 
      [ [ 1, E(5)+2*E(5)^2+2*E(5)^3+E(5)^4, 0 ], [ 0, -1, 0 ], 
          [ 0, -1, 1 ] ], [ [ 1, 0, 0 ], [ 0, 1, -1 ], [ 0, 0, -1 ] ] ]

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

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