A Nekrasov-Okounkov formula for Macdonald polynomials
Combinatorics
2018-08-07 v3 Mathematical Physics
Algebraic Geometry
math.MP
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.
Cite
@article{arxiv.1606.04613,
title = {A Nekrasov-Okounkov formula for Macdonald polynomials},
author = {Eric M. Rains and S. Ole Warnaar},
journal= {arXiv preprint arXiv:1606.04613},
year = {2018}
}
Comments
24 pages; Revised version includes an alternative proof (suggested by Jim Bryan) of an elliptic Nekrasov-Okounkov formula based on the equivariant DMVV formula. In v3 some final corrections have been carried out