Linear Algebra and its Applications | 2021
Congruence subgroups and orthogonal groups
Abstract
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 S O 0 ( 2 , n ) , n = 3 , 4 , 6 . The proof is based on an application of linear algebra adapted to the number theoretical needs.