A Nekrasov-Okounkov formula for Macdonald polynomials

Published 15 Jun 2016 in math.CO, math-ph, math.AG, and math.MP | (1606.04613v3)

Abstract: We prove a Macdonald polynomial analogue of the celebrated Nekrasov-Okounkov hook-length formula from the theory of random partitions. As an application we obtain a proof of one of the main conjectures of Hausel and Rodriguez-Villegas from their work on mixed Hodge polynomials of the moduli space of stable Higgs bundles on Riemann surfaces.

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