{"paper":{"title":"Arithmetic groups, base change, and representation growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Klopsch, Christopher Voll, Nir Avni, Uri Onn","submitted_at":"2011-10-27T14:38:30Z","abstract_excerpt":"Consider an arithmetic group $\\mathbf{G}(O_S)$, where $\\mathbf{G}$ is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of $S$-integers $O_S$ of a number field $K$ with respect to a finite set of places $S$. For each $n \\in \\mathbb{N}$, let $R_n(\\mathbf{G}(O_S))$ denote the number of irreducible complex representations of $\\mathbf{G}(O_S)$ of dimension at most $n$. The degree of representation growth $\\alpha(\\mathbf{G}(O_S)) = \\lim_{n \\rightarrow \\infty} \\log R_n(\\mathbf{G}(O_S)) / \\log n$ is finite if and only if $\\mathbf{G}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6092","kind":"arxiv","version":4},"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"}