{"paper":{"title":"On the U-module Structure of the Unipotent Specht Modules of Finite General Linear Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Qiong Guo","submitted_at":"2013-04-16T09:10:03Z","abstract_excerpt":"Let $q$ be a prime power, $G=GL_n(q)$ and let $U\\leqslant G$ be the subgroup of (lower) unitriangular matrices in $G$. For a partition $\\lambda$ of $n$ denote the corresponding unipotent Specht module over the complex field $\\C$ for $G$ by $S^\\lambda$. It is conjectured that for $c\\in \\Z_{\\geqslant 0}$ the number of irreducible constituents of dimension $q^c$ of the restriction $\\RRes^{G}_U(S^\\lambda)$ of $S^\\lambda$ to $U$ is a polynomial in $q$ with integer coefficients depending only on $c$ and $\\lambda$, not on $q$. In the special case of the partition $\\lambda=(1^n)$ this implies a longst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4370","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"}