Congruence subgroups and orthogonal groups

Abstract

We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2 and the discriminant kernels of special orthogonal groups SO0(2,n), n=3,4,6. The proof is based on an application of linear algebra adapted to the number theoretical needs.