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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conjugacy Classes of $SU(h,\mathcal{O}_S)$ in $SL(2,\mathcal{O}_S)$


Author: Donald G. James
Journal: Trans. Amer. Math. Soc. 351 (1999), 825-835
MSC (1991): Primary 11E57, 11F06, 20G30
DOI: https://doi.org/10.1090/S0002-9947-99-02066-8
MathSciNet review: 1451605
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Abstract: Let $K$ be a quadratic extension of a global field $F$, of characteristic not two, and $\mathcal{O}_S$ the integral closure in $K$ of a Dedekind ring of $S$-integers $\mathfrak{O}_S$ in $F$. Then $PSL(2, \mathcal{O}_S)$ is isomorphic to the spinorial kernel $O'(L)$ for an indefinite quadratic $\mathfrak{O}_S$-lattice $L$ of rank 4. The isomorphism is used to study the conjugacy classes of unitary groups $PSU(h,\mathcal{O}_S)$ of primitive odd binary hermitian matrices $h$ under the action of $PSL(2, \mathcal{O}_S)$.


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Additional Information

Donald G. James
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email: james@math.psu.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02066-8
Received by editor(s): January 24, 1996
Received by editor(s) in revised form: February 20, 1997
Additional Notes: The author was supported by NSF grant DMS-95-00533.
Article copyright: © Copyright 1999 American Mathematical Society