{"paper":{"title":"An explicit exotic representation of a rank-one simple Lie group via convex bodies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.RT"],"primary_cat":"math.GR","authors_text":"David Xu, Fran\\c{c}ois Fillastre, Yusen Long","submitted_at":"2025-12-13T15:52:00Z","abstract_excerpt":"In [DP12], Delzant and Py showed that there exist continuous irreducible isometric actions of $\\mathrm{PSL}_2(\\mathbb{R})$ on the infinite-dimensional hyperbolic space $\\mathbb{H}^\\infty$. Such continuous irreducible actions do not exist on the hyperbolic spaces $\\mathbb{H}^n$ when $n>2$ and their associated embeddings $\\mathbb{H}^2 \\to \\mathbb{H}^\\infty$ given by the orbit maps were later called \\emph{exotic} by Monod and Py in [MP14]. In this article, we produce a continuous and irreducible representation of $\\mathrm{PSL}_2(\\mathbb{R})\\to \\mathrm{Isom}(\\mathbb{H}^\\infty)$ using the hyperboli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.12369","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.12369/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}