  Motivated by permutation statistics, we define for any complex reflection
group W a family of bivariate generating functions. They are defined either in
terms of Hilbert series for W-invariant polynomials when W acts diagonally on
two sets of variables, or equivalently, as sums involving the fake degrees of
irreducible representations for W. It is also shown that they satisfy a
``bicyclic sieving phenomenon'', which combinatorially interprets their values
when the two variables are set equal to certain roots of unity.
