Published August 2018
| Version Submitted
Journal Article
Open
A Nekrasov–Okounkov formula for Macdonald polynomials
Creators
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1.
California Institute of Technology
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2.
University of Queensland
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.
Additional Information
© 2017 Springer Science+Business Media, LLC. Received: 18 December 2016; Accepted: 09 September 2017; First Online: 22 September 2017. Work supported by the National Science Foundation (Grant Number DMS-1001645) and the Australian Research Council. The second author is grateful to Masoud Kamgarpour for pointing out the papers of Hausel and Rodriguez-Villegas [22], and Hausel, Letellier and Rodriguez-Villegas [20, 21] on mixed Hodge polynomials, and to Dennis Stanton for helpful discussions on p-core partitions. We thank Fernando Rodriguez-Villegas for sending us a preliminary version of his paper [6] with Carlsson, which contains a different proof of Conjecture 1.1 based on the Carlsson–Nekrasov–Okounkov vertex operator [5]. We also thank Amer Iqbal for alerting us to the connection between our work and [24] and Jim Bryan for explaining the work of Waelder, which implies the elliptic Nekrasov–Okounkov formula described in the appendix. We thank the two referees for their helpful comments and corrections.Attached Files
Submitted - 1606.04613.pdf
Files
1606.04613.pdf
Additional details
Identifiers
- Eprint ID
- 81746
- Resolver ID
- CaltechAUTHORS:20170922-130437528
Related works
- Describes
- https://arxiv.org/abs/1606.04613 (URL)
Funding
- NSF
- DMS-1001645
- Australian Research Council
Dates
- Created
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2017-09-22Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department