82.8 SchurElement

SchurElement( H, phi )

returns the constants arising from the Schur relations for the irreducible character phi of the Iwahori-Hecke algebra H. phi should be specified by its parameter (see CharParams in section Operations and functions for Coxeter groups) .

    gap> u := X( Rationals );; u.name := "u";;
    gap> v := X( LaurentPolynomialRing( Rationals ) );; v.name := "v";;
    gap> H := Hecke( CoxeterGroup( "G", 2 ), [ u ^ 2, v ^ 2 ], [ u, v ] );
    Hecke(CoxeterGroup("G", 2),[ u^2, v^2 ],[ u, v ])
    gap> SchurElement( H, [ [ 1, 3, "'" ] ] );
    (u^(-4) + u^(-6))*v^6 + (u^(-2) + 2*u^(-4) + u^(-6))*v^4 + (1 + 2*u^(
    -2) + u^(-4))*v^2 + (1 + u^(-2))

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

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