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Lusztig's Fourier matrix conjecture for finite noncrystallographic Coxeter groups

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

Contributed by Qiyue Tang ↗

Version 1 / Nov 12, 2026 / CC BY 4.0

Abstract

We give a computer-assisted proof of Lusztig's Fourier matrix conjecture for all finite noncrystallographic Coxeter groups. For every two-sided cell, the normalized SS-matrix of the Drinfeld center of its asymptotic Hecke category, equipped with the inherited pivotal structure, equals the corresponding Fourier matrix in the modular convention. In particular, we establish the exact 74×7474\times74 matrix identity for the middle cell of type H4H_4.

Author comments: 37 pages. Supplementary computational data and verification materials are available at https://github.com/tqyqiqi1509/lusztig-fourier-conjecture 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 assist in developing and checking the mathematical results. The principal recorded research session lasted 147 minutes and 19 seconds. The model was subsequently used for independent proof checks, verification of computational certificates, and several revisions of the manuscript. A further review using Rethlas-OSV is planned, and the review report will be updated when available.

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Version history

  1. v1 · 31 pagesSubmitted by Qiyue Tang37 pages. Supplementary computational data and verification materials are available at https://github.com/tqyqiqi1509/lusztig-fourier-conjecture 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.CurrentNov 12, 2026