{"paper":{"title":"The irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(p^f)$ and $\\mathrm{E}_6(p^f)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alessandro Paolini, Kay Magaard, Tung Le","submitted_at":"2017-12-26T13:11:54Z","abstract_excerpt":"We parametrize the set of irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(q)$ and $\\mathrm{E}_6(q)$, for an arbitrary power $q$ of any prime $p$. In particular, we establish that the parametrization is uniform for $p \\ge 3$ in type $\\mathrm{D}_6$ and for $p \\ge 5$ in type $\\mathrm{E}_6$, while the prime $2$ in type $\\mathrm{D}_6$ and the primes $2,$ $3$ in type $\\mathrm{E}_6$ yield character degrees of the form $q^m/p^i$ which force a departure from the generic situations. Also for the first time in our analysis we see a family of irreducible characters "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09263","kind":"arxiv","version":1},"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"}