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The Quantum Kazhdan–Lusztig Conjecture for Quantum Loop Algebras

Primarily AI-generated textHuman understanding: no partsmath.RT — Representation Theorymath.QA — Quantum Algebra

Contributed by Qiyue Tang ↗

Version 1 / Nov 12, 2026 / CC BY 4.0

Abstract

We prove the quantum Kazhdan–Lusztig conjecture for finite-dimensional type 1 representations of untwisted quantum loop algebras at every non-root-of-unity complex parameter.

Author comments: By posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.

Provenance statement

GPT-6-Pro was used for approximately 6.1 hours in one research round. GPT-6-Pro was also used to review the mathematical arguments and to polish the manuscript. An additional review by Rethlas-OSV will be incorporated at a later stage.

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Version history

  1. v1 · 76 pagesSubmitted by Qiyue TangBy posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.CurrentNov 11, 2026