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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Representations of anisotropic unitary groups


Author: Donald G. James
Journal: Trans. Amer. Math. Soc. 306 (1988), 791-804
MSC: Primary 11E57; Secondary 11E10, 20G05
MathSciNet review: 933318
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Abstract: Let $ SU(f)$ be the special unitary group of an anisotropic hermitian form $ f$ over a field $ k$. Assume $ f$ represents only one norm class in $ k$. The representations $ \alpha :\,SU(f) \to SL(n,\,R)$ are characterized when $ R$ is a commutative ring with $ 2$ not a zero divisor and $ n = \dim f \geqslant 3$ with $ n \ne 4,\,6$. In particular, a partial classification of the normal subgroups of $ SU(f)$ is given when $ k$ is the function field $ {\mathbf{C}}(X)$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0933318-3
PII: S 0002-9947(1988)0933318-3
Article copyright: © Copyright 1988 American Mathematical Society