{"paper":{"title":"Maximal representations, non Archimedean Siegel spaces, and buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.GR","authors_text":"Marc Burger, Maria Beatrice Pozzetti","submitted_at":"2015-09-03T17:54:51Z","abstract_excerpt":"Let $\\mathbb F$ be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in ${\\rm Sp}(2n,\\mathbb F)$. We show that ultralimits of maximal representations in ${\\rm Sp}(2n,\\mathbb R)$ admit such a framing, and that all maximal framed representations satisfy a suitable generalisation of the classical Collar Lemma. In particular this establishes a Collar Lemma for all maximal representations into ${\\rm Sp}(2n,\\mathbb R)$. We then describe a procedure to get from representations in ${\\rm Sp}(2n,\\mathbb F)$ interesting a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01184","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"}