{"paper":{"title":"$U_n(q)$ acting on flags and supercharacters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Qiong Guo, Richard Dipper","submitted_at":"2014-12-10T17:26:51Z","abstract_excerpt":"Let $U=U_n(q)$ be the group of lower unitriangular $n \\times n$-matrices with entries in the field $\\mathbb F_q$ with $q$ elements for some prime power $q$ and $n \\in \\mathbb N$. We investigate the restriction to $U$ of the permutation action of $GL_n(q)$ on flags in the natural $GL_n(q)$-module $\\mathbb F_q^n$. Applying our results to the special case of flags of length two we obtain a complete decomposition of the permutation representation of $GL_n(q)$ on the cosets of maximal parabolic subgroups into irreducible $\\mathbb C U$-modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3376","kind":"arxiv","version":4},"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"}