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Projected stated (SL_n)-skein algebras and the Huang–Wang conjectures

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.RT — Representation Theory

Contributed by Qiyue Tang ↗

Version 1 / Nov 02, 2026 / CC BY 4.0

Abstract

We prove Conjectures 1.5 and 1.6 of Min Huang and Zhihao Wang: the projected stated (SL_n)-skein algebra equals its quantum cluster and upper cluster algebras, and the specified exchangeable variables generate it over the frozen Laurent coefficient algebra. The results hold for triangulable unpunctured marked surfaces with at least two boundary marked points per connected component, over every coefficient domain and parameter in the conjectures.

Provenance statement

The main results of this paper were generated in a ChatGPT-6-Pro conversation lasting approximately 262 minutes of elapsed time. The author supplied the research materials. Codex subsequently reviewed the arguments, checked references, and revised the exposition. The manuscript was also reviewed using Rethlas–OSV, which implements the OSVerify framework of Nie, Ye, Liu, Wang, Ermon, and Zou.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentNov 01, 2026