{"paper":{"title":"Classification of Affine Symmetry Groups of Orbit Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.RT"],"primary_cat":"math.GR","authors_text":"Erik Friese, Frieder Ladisch","submitted_at":"2016-08-23T15:14:48Z","abstract_excerpt":"Let $G$ be a finite group acting linearly on a vector space $V$. We consider the linear symmetry groups $\\operatorname{GL}(Gv)$ of orbits $Gv\\subseteq V$, where the \\emph{linear symmetry group} $\\operatorname{GL}(S)$ of a subset $S\\subseteq V$ is defined as the set of all linear maps of the linear span of $S$ which permute $S$. We assume that $V$ is the linear span of at least one orbit $Gv$. We define a set of \\emph{generic points} in $V$, which is Zariski-open in $V$, and show that the groups $\\operatorname{GL}(Gv)$ for $v$ generic are all isomorphic, and isomorphic to a subgroup of every sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06539","kind":"arxiv","version":4},"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"}