{"paper":{"title":"Finite traces and representations of the group of infinite matrices over a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.RT","authors_text":"Anatoly Vershik, Sergei Kerov, Vadim Gorin","submitted_at":"2012-09-22T00:38:41Z","abstract_excerpt":"The article is devoted to the representation theory of locally compact infinite-dimensional group $\\mathbb{GLB}$ of almost upper-triangular infinite matrices over the finite field with $q$ elements. This group was defined by S.K., A.V., and Andrei Zelevinsky in 1982 as an adequate $n=\\infty$ analogue of general linear groups $\\mathbb{GL}(n,q)$. It serves as an alternative to $\\mathbb{GL}(\\infty,q)$, whose representation theory is poor.\n  Our most important results are the description of semi-finite unipotent traces (characters) of the group $\\mathbb{ GLB}$ via certain probability measures on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4945","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"}