{"paper":{"title":"Irreducible representations of unipotent subgroups of symplectic and unitary groups defined over rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Szechtman","submitted_at":"2015-07-27T14:17:41Z","abstract_excerpt":"Let $A$ be a ring with $1\\neq 0$, not necessarily finite, endowed with an involution~$*$, that is, an anti-automorphism of order $\\leq 2$. Let $H_n(A)$ be the additive group of all $n\\times n$ hermitian matrices over $A$ relative to $*$. Let ${\\mathcal U}_n(A)$ be the subgroup of $\\mathrm{GL}_n(A)$ of all upper triangular matrices with 1's along the main diagonal. Let $P=H_n(A)\\rtimes {\\mathcal U}_n(A)$, where ${\\mathcal U}_n(A)$ acts on $H_n(A)$ by $*$-congruence transformations. We may view $P$ as a unipotent subgroup of either a symplectic group $\\mathrm{Sp}_{2n}(A)$, if $*=1_A$ (in which c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07410","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"}