Localization and a generalization of MacDonald's inner product

2013/05/03 by Erik Carlsson, Carlsson, Erik
Mathematics · #05E05 #19L47 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E05 #msc:19L47

paper · pdf · doi:10.48550/arxiv.1305.0778

10 pages, no figures

arxiv created 2013/05/03 · arxiv updated 2013/05/06

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 \citeCar, which bounds the torus characters of the higher Çech 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 \citeMac, making this limit suitable replacement for the norm squared of one, the usual normalizing constant.

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