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A proof of the Hausel–Rodriguez-Villegas conjecture

Primarily AI-generated textHuman understanding: no partsmath.AG — Algebraic Geometrymath.RT — Representation Theory

Contributed by Qiyue Tang ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We prove the Hausel–Rodriguez-Villegas conjecture on the mixed Hodge polynomials of primitive-twisted GLn\mathrm{GL}_n character varieties.

Author comments: I am posting this manuscript to share the mathematical results themselves. In doing so, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in checking the arguments or preparing a finished account, and I believe the eventual scholarly credit should go to those who undertake that work.

Provenance statement

GPT-6-Pro was used to develop the mathematical arguments over two research sessions totalling approximately 22 hours of recorded wall-clock time. GPT-6-Pro was also used to review the arguments and polish the manuscript. A review using Rethlas-OSV will be added in a subsequent revision.

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Version history

  1. v1 · 67 pagesSubmitted by Qiyue TangI am posting this manuscript to share the mathematical results themselves. In doing so, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in checking the arguments or preparing a finished account, and I believe the eventual scholarly credit should go to those who undertake that work.CurrentNov 13, 2026