{"paper":{"title":"Notes on affine isometric actions of discrete groups","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Yurii A. Neretin","submitted_at":"1997-12-20T12:55:16Z","abstract_excerpt":"Consider a lattice $\\Gamma$ in a group $G = SL_2(\\R), SO(1,n), SU(1,n)$, $SL_2(\\Q_p)$. We discuss actions of $\\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its restriction to $\\Gamma$ is irreducible. We prove the existence of canonical irreducible affine isometric actions of $\\Gamma$ associated to actions of $\\Gamma$ on $\\R$- trees. Using such actions we construct irreducible representations of semigroup of probabilistic measures on $\\Gamma$ and construct the series of representations of the groups of diffeomorphisms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9712009","kind":"arxiv","version":1},"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"}