{"paper":{"title":"Representation equivalent Bieberbach groups and strongly isospectral flat manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SP"],"primary_cat":"math.DG","authors_text":"Emilio A. Lauret","submitted_at":"2012-10-02T19:48:30Z","abstract_excerpt":"Let $\\Gamma_1$ and $\\Gamma_2$ be Bieberbach groups contained in the full isometry group $G$ of $\\mathbb{R}^n$. We prove that if the compact flat manifolds $\\Gamma_1\\backslash\\mathbb{R}^n$ and $\\Gamma_2\\backslash\\mathbb{R}^n$ are strongly isospectral then the Bieberbach groups $\\Gamma_1$ and $\\Gamma_2$ are representation equivalent, that is, the right regular representations $L^2(\\Gamma_1\\backslash G)$ and $L^2(\\Gamma_2\\backslash G)$ are unitarily equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0894","kind":"arxiv","version":2},"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"}