{"id":"hexagon/2610.00614","pdf":"https://hexagonmath.org/pdf/2610.00614v1","url":"https://hexagonmath.org/abs/2610.00614v1","tags":["math.QA","math.RA","msc:13F60","msc:14M15","msc:17B10","Cluster Algebra"],"score":0,"title":"The Mirković–Vilonen basis and cluster pointedness","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.RT","summary":"We prove that the Mirković–Vilonen basis of $\\mathbb{C}[N]$ contains every cluster monomial and that each of its elements is $g$-pointed in every cluster, where $N$ is a maximal unipotent subgroup of a complex semisimple group. This resolves Conjecture 6.6 in Kamnitzer’s ICM 2022 survey.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}