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A proof of Lusztig’s conjectures for extended affine Weyl groups

Primarily AI-generated textHuman understanding: no partsmath.RT — Representation Theorymath.CO — Combinatoricsmath.GR — Group Theory

Contributed by Qiyue Tang ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We prove Lusztig’s conjectures P1–P15 for extended affine Weyl groups with positive integer-valued weight functions.

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 for more than 110 hours of documented research-session time across fourteen rounds of work on Lusztig’s conjectures P1–P15. It was also used to review and polish the manuscript. A review by Rethlas-OSV will be added later.

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Version history

  1. v1 · 57 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 12, 2026