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dc.contributor.authorCruickshank, J.
dc.contributor.authorSzechtman, F.
dc.date.accessioned2018-09-20T16:04:30Z
dc.date.available2018-09-20T16:04:30Z
dc.date.issued2018-04-01
dc.identifier.citationCruickshank, J. Szechtman, F. (2018). Generators and relations for the unitary group of a skew hermitian form over a local ring. Linear Algebra and its Applications 552 , 1-28
dc.identifier.issn0024-3795
dc.identifier.urihttp://hdl.handle.net/10379/10970
dc.description.abstractLet (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. 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 is used to prove that the reduction homomorphisms SU(2m, S) -> SU(2m, (S) over tilde) and U(2m, 5) -> U(2m, (S) over tilde) are surjective for any factor ring S of S. The corresponding results for the symplectic group Sp(2m, R) are obtained as corollaries when * is the identity. Published by Elsevier Inc.
dc.publisherElsevier BV
dc.relation.ispartofLinear Algebra and its Applications
dc.subjectunitary group
dc.subjectbruhat decomposition
dc.subjectgroup presentation
dc.subjecttransvection
dc.subjectgroup sl(asterisk) 2
dc.subjectfinite rings
dc.subjecttheorem
dc.titleGenerators and relations for the unitary group of a skew hermitian form over a local ring
dc.typeArticle
dc.identifier.doi10.1016/j.laa.2018.04.001
dc.local.publishedsourcehttp://arxiv.org/pdf/1710.11574
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