{"paper":{"title":"Characters of the Norm-One Units of Local Division Algebras of Prime Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shai Shechter","submitted_at":"2015-12-08T13:10:00Z","abstract_excerpt":"We give an explicit construction of all complex continuous irreducible characters of the group ${\\rm SL}_1(D)$, where $D$ is a division algebra of prime degree $\\ell$ over a local field of odd residual characteristic different than $\\ell$. For $\\ell$ odd, we show that all such characters of ${\\rm SL}_1(D)$ are induced from linear characters of compact-open subgroups of ${\\rm SL}_1(D)$. We also compute an explicit formula for the representation zeta function of ${\\rm SL}_1(D)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02448","kind":"arxiv","version":3},"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"}