{"paper":{"title":"On the $\\ell$-modular composition factors of the Steinberg representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Meinolf Geck","submitted_at":"2015-04-16T09:31:23Z","abstract_excerpt":"Let $G$ be a finite group of Lie type and $\\St_k$ be the Steinberg representation of $G$, defined over a field $k$. We are interested in the case where $k$ has prime characteristic~$\\ell$ and $\\St_k$ is reducible. Tinberg has shown that the socle of $\\St_k$ is always simple. We give a new proof of this result in terms of the Hecke algebra of $G$ with respect to a Borel subgroup and show how to identify the simple socle of $\\St_k$ among the principal series representations of~$G$. Furthermore, we determine the composition length of $\\St_k$ when $G=\\GL_n(q)$ or $G$ is a finite classical group an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04157","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"}