82.4 HeckeCharValues

HeckeCharValues( T [,irreds])

T is an element of an Iwahori-Hecke algebra (expressed in any basis) and irreds is a set of irreducible characters of the algebra (given as vectors). HeckeCharValues returns the values of irreds on the element T (the method used is to convert to the T basis, and then use HeckeClassPolynomials). If irreds is not given, all character values are returned.

    gap> q := X( Rationals );; q.name := "q";;
    gap> H := Hecke( CoxeterGroup( "B", 2 ), q ^ 2, q );;
    gap> HeckeCharValues( Basis( H, "C'" )( 1, 2, 1 ) );
    [ 0*q^0, q + q^(-1), 0*q^0, q^3 + 2*q + 2*q^(-1) + q^(-3), 
      -q - q^(-1) ]