{"paper":{"title":"Characters of algebraic groups over number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.RT"],"primary_cat":"math.GR","authors_text":"Bachir Bekka, Camille Francini","submitted_at":"2020-02-18T11:30:51Z","abstract_excerpt":"Let $k$ be a number field, $\\mathbf{G}$ an algebraic group defined over $k$, and $\\mathbf{G}(k)$ the group of $k$-rational points in $\\mathbf{G}.$ We determine the set of functions on $\\mathbf{G}(k)$ which are of positive type and conjugation invariant, under the assumption that $\\mathbf{G}(k)$ is generated by its unipotent elements. An essential step in the proof is the classification of the $\\mathbf{G}(k)$-invariant ergodic probability measures on an adelic solenoid naturally associated to $\\mathbf{G}(k);$ this last result is deduced from Ratner's measure rigidity theorem for homogeneous spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.07497","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.07497/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"}