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A proof of Lusztig's connectedness conjecture in finite type

Primarily AI-generated textHuman understanding: no partsmath.RT — Representation Theorymath.CO — Combinatorics

Contributed by Qiyue Tang ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We prove that every equal-parameter Kazhdan–Lusztig left cell in a finite Weyl group is connected by simple left multiplications.

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 in a broader investigation of Lusztig's connectedness conjecture over twelve research sessions, with approximately 88 hours of documented research-session time in total. This paper presents the finite-type part of that investigation. GPT-6-Pro was also used to review the mathematical arguments and edit the manuscript. A review by Rethlas-OSV will be added in a subsequent update.

References

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Version history

  1. v1 · 30 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