Localization and a generalization of MacDonalds inner product

We find a limit formula for a generalization of MacDonalds inner product in finitely many variables, using equivariant localization on the Grassmannian variety, and the main lemma from cite{Car}, which bounds the torus characters of the higher c{C}ech cohomology groups. We show that the MacDonald inner product conjecture of type $A$ follows from a special case, and the Pieri rules section of MacDonalds book cite{Mac}, making this limit suitable replacement for the norm squared of one, the usual normalizing constant.