A Nekrasov-Okounkov formula for Macdonald polynomials

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.

arXiv comment24 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

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Cited by in corpus (8)

• Black Hole Entropy from Quantum Mechanics
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Free field theory and observables of periodic Macdonald processes
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Quasi-Hopf twist and elliptic Nekrasov factor
• Modular Nekrasov-Okounkov formulas
• On Smith normal forms of $q$-Varchenko matrices
• Some combinatorial interpretations of the Macdonald identities for affine root systems