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The Mirković–Vilonen basis and cluster pointedness

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

Contributed by Qiyue Tang ↗

Version 1 / Oct 29, 2026 / CC BY 4.0

Abstract

We prove that the Mirković–Vilonen basis of C[N]\mathbb{C}[N] contains every cluster monomial and that each of its elements is gg-pointed in every cluster, where NN is a maximal unipotent subgroup of a complex semisimple group. This resolves Conjecture 6.6 in Kamnitzer’s ICM 2022 survey.

Provenance statement

The results were developed in an approximately 88-minute Codex session using GPT-6-Astra at high reasoning effort, followed by approximately three hours of research using Chat-6-Pro. Codex subsequently used its mathematical-paper-writing skill to revise the manuscript and conduct adversarial mathematical reviews. The manuscript passed an AI-assisted review using Rethlas-OSV.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 28, 2026