{"paper":{"title":"Decomposition of Tensor Products of Modular Irreducible Representations for $SL_3$: the $p \\geq 5$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"C. Bowman, S. Martin, S. R. Doty","submitted_at":"2011-11-24T16:21:20Z","abstract_excerpt":"We study the structure of the indecomposable direct summands of tensor products of two restricted simple $SL_3(K)$-modules, where $K$ is an algebraically closed field of characteristic $p \\geq 5$. We give a characteristic-free algorithm for the computation of the decomposition of such a tensor product into indecomposable modules.\n  The $p<5$ case for $\\SL_3(K)$ was studied in the authors' earlier paper. In this paper we show that for characteristics $p\\geq 5$ all the indecomposable summands are rigid, in contrast to the situation in characteristic 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5811","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"}