82.6 PoincarePolynomial

PoincarePolynomial( H )

The Poincaraccent19 e polynomial of the Hecke algebra H, which is equal to SchurElements(H)[ind] where ind is the position of the 1-dimensional index representation in the character table of H, that is, the representation which maps T_{s_i} to the corresponding parameter q_i.

    gap> q := X( Rationals );; q.name := "q";;
    gap> W := CoxeterGroup( "G", 2 );; H := Hecke( W, q );
    Hecke(CoxeterGroup("G", 2),[ q, q ],[  ])
    gap> PoincarePolynomial( H );
    q^6 + 2*q^5 + 2*q^4 + 2*q^3 + 2*q^2 + 2*q + 1 

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

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