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Unitary groups over local rings

CRUICKSHANK, J.
; 
HERMAN, A.
; 
QUINLAN, R.
; 
SZECHTMAN, F.
Repository DOI
Publication Date
2014-03-01
Keywords
hermitian form, unitary group, local ring, involution, ramified and unramified extension, weil representations
Type
Article
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Citation
CRUICKSHANK, J. HERMAN, A.; QUINLAN, R.; SZECHTMAN, F. (2014). Unitary groups over local rings. Journal of Algebra and Its Applications 13 (2),
Abstract
We study hermitian forms and unitary groups defined over a local ring, not necessarily commutative, equipped with an involution. When the ring is finite we obtain formulae for the order of the unitary groups as well as their point stabilizers, and use these to compute the degrees of the irreducible constituents of the Weil representation of a unitary group associated to a ramified quadratic extension of a finite local ring.
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Publisher
World Scientific Pub Co Pte Lt
Publisher DOI
10.1142/s021949881350093x
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)