{"paper":{"title":"V-systems, holonomy Lie algebras and logarithmic vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"A.P. Veselov, M.V. Feigin","submitted_at":"2014-07-31T22:37:39Z","abstract_excerpt":"It is shown that the description of certain class of representations of the holonomy Lie algebra associated to hyperplane arrangement $\\Delta$ is essentially equivalent to the classification of $\\vee$-systems associated to $\\Delta.$ The flat sections of the corresponding $\\vee$-connection can be interpreted as vector fields, which are both logarithmic and gradient. We conjecture that the hyperplane arrangement of any $\\vee$-system is free in Saito's sense and show this for all known $\\vee$-systems and for a special class of $\\vee$-systems called harmonic, which includes all Coxeter systems. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2424","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"}