77.2 ReflectionCharValue

ReflectionCharValue( W, w )

Let V be the vector space on which the Coxeter group W acts, and let w be the linear automorphism of V induced by a permutation of the roots (acting trivially on the orthogonal of the roots if W.rankW.semisimpleRank). ReflectionCharValue returns the trace of w on V.

    gap> W := CoxeterGroup( "A", 3 );
    CoxeterGroup("A", 3)
    gap> List( Elements( W ), x -> ReflectionCharValue( W, x ) );
    [ 3, 1, -1, 0, -1, -1, 0, 1, 0, -1, 1, 0, 1, -1, 0, 1, -1, -1, 0, -1, 
      1, 0, -1, 0 ] 

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

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