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