  We describe a way to study and compute Pieri rules for wreath Macdonald
polynomials using the quantum toroidal algebra. The Macdonald pairing can be
naturally generalized to the wreath setting, but the wreath Macdonald
polynomials are no longer collinear with their duals. We establish the
relationship between these dual polynomials and the quantum toroidal algebra,
and we outline a way to compute norm formulas. None of the aforementioned
formulas are successfully computed in this paper.
