{"paper":{"title":"Generators and relations for the unitary group of a skew hermitian form over a local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Fernando Szechtman, James Cruickshank","submitted_at":"2017-10-31T16:45:09Z","abstract_excerpt":"Let $(S,*)$ be an involutive local ring and let $U(2m,S)$ be the unitary group associated to a nondegenerate skew hermitian form defined on a free $S$-module of rank $2m$. A presentation of $U(2m,S)$ is given in terms of Bruhat generators and their relations. This presentation is used to construct an explicit Weil representation of the symplectic group $Sp(2m,R)$ when $S=R$ is commutative and $*$ is the identity.\n  When $S$ is commutative but $*$ is arbitrary with fixed ring $R$, an elementary proof that the special unitary group $SU(2m,S)$ is generated by unitary transvections is given. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11574","kind":"arxiv","version":3},"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"}