{"paper":{"title":"Representations of McLain groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Allen Herman, Fernando Szechtman, Mohammad Izadi","submitted_at":"2015-06-19T23:56:16Z","abstract_excerpt":"Basic modules of McLain groups $M=M(\\Lambda,\\leq, R)$ are defined and investigated. These are (possibly infinite dimensional) analogues of Andr\\'e's supercharacters of $U_n(q)$. The ring $R$ need not be finite or commutative and the field underlying our representations is essentially arbitrary: we deal with all characteristics, prime or zero, on an equal basis. The set $\\Lambda$, totally ordered by $\\leq$, is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06184","kind":"arxiv","version":12},"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"}