{"paper":{"title":"An effective Lie--Kolchin theorem for quasi-unipotent matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Feng Luo, Hongbin Sun, Thomas Koberda","submitted_at":"2019-04-01T18:03:46Z","abstract_excerpt":"We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\\in\\mathrm{GL}_m(\\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for all $k\\geq0$ the matrix $AB^k$ is also quasi--unipotent. Then $A$ and $B$ have a common eigenvector. In particular, $\\langle A,B\\rangle<\\mathrm{GL}_m(\\mathbb{C})$ is a solvable subgroup. We give applications of this result to the representation theory of mapping class groups of orientable surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01037","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}