83.8 Hecke elements of the primed $C$ basis

Basis( H, "C'" )

returns a function which gives the C^prime-basis of the (one parameter generic) Iwahori-Hecke algebra H (see cite[(5.1)]Lus85). This is defined by [ C_x^prime := sum_y leq x P_x,y(v^2)v^-l(x) T_y quad mbox for every x in W.] We have C_x^prime=Alt(C_x) for all x in W (see AltInvolution in section Operations for Hecke elements of the $T$ basis).

    gap> v := X( Rationals );; v.name := "v";;
    gap> H := Hecke( CoxeterGroup( "B", 2 ), v ^ 2, v );;
    gap> h := Basis( H, "C'" )( 1 );
    C'(1)
    gap> h2 := h * h;
    (v+v^-1)C'(1)
    gap> Basis( H, "T" )( h2 );
    (1+v^-2)T()+(1+v^-2)T(1) 

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

Previous Up Top Next
Index