FakeDegrees( W, q )
returns a list holding the fake degrees of W as a reflection group on
the vector space V on which it acts, evaluated at q. These are the
graded multiplicities of the irreducible characters of W in the
quotient SV/I where SV is the symmetric algebra of V and I is the
ideal generated by the homogeneous invariants of positive degree in SV.
The ordering of the result corresponds to the ordering of the characters
in CharTable(W).
gap> q := X( Rationals );; q.name := "q";;
gap> FakeDegrees( CoxeterGroup( "A", 2 ), q );
[ q^3, q^2 + q, q^0 ]
This function requires the package "chevie" (see RequirePackage).
GAP 3.4.4