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Conjugacy Classes of

Authors:	Donald G James

Institution:	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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