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Conjugacy Classes of

Authors:	Donald G. James

Affiliation:	Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

Abstract:	Let be a quadratic extension of a global field , of characteristic not two, and $mathcal{O}_S$ the integral closure in of a Dedekind ring of -integers $mathfrak{O}_S$ in . Then $PSL(2, mathcal{O}_S)$ is isomorphic to the spinorial kernel for an indefinite quadratic $mathfrak{O}_S$ -lattice 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 under the action of $PSL(2, mathcal{O}_S)$ .

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