{"paper":{"title":"The blocks and weights of finite special linear and unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Zhicheng Feng","submitted_at":"2018-05-17T07:42:19Z","abstract_excerpt":"This paper has two main parts. Firstly, we give a classification of the $\\ell$-blocks of finite special linear and unitary groups $SL_n(\\epsilon q)$ in the non-defining characteristic $\\ell\\ge 3$. Secondly, we describe how the $\\ell$-weights of $SL_n(\\epsilon q)$ can be obtained from the $\\ell$-weights of $GL_n(\\epsilon q)$ when $\\ell\\nmid\\mathrm{gcd}(n,q-\\epsilon)$, and verify the Alperin weight conjecture for $SL_n(\\epsilon q)$ under the condition $\\ell\\nmid\\mathrm{gcd}(n,q-\\epsilon)$. As a step to establish the Alperin weight conjecture for all finite groups, we prove the inductive blockwis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06633","kind":"arxiv","version":2},"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"}