{"paper":{"title":"Multiderivations of Coxeter arrangements","license":"","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Hiroaki Terao","submitted_at":"2000-11-29T01:21:38Z","abstract_excerpt":"Let $V$ be an $\\ell$-dimensional Euclidean space. Let $G \\subset O(V)$ be a finite irreducible orthogonal reflection group. Let ${\\cal A}$ be the corresponding Coxeter arrangement. Let $S$ be the algebra of polynomial functions on $V.$ For $H \\in {\\cal A}$ choose $\\alpha_H \\in V^*$ such that $H = {\\rm ker}(\\alpha_H).$ For each nonnegative integer $m$, define the derivation module $\\sD^{(m)}({\\cal A}) = \\{\\theta \\in {\\rm Der}_S | \\theta(\\alpha_H) \\in S \\alpha^m_H\\}$. The module is known to be a free $S$-module of rank $\\ell$ by K. Saito (1975) for $m=1$ and L. Solomon-H. Terao (1998) for $m=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011247","kind":"arxiv","version":6},"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"}