Congruence Subgroups and Orthogonal Groups
Number Theory
2021-02-02 v2
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 SO 0 (2, n), n = 3, 4, 6. The proof is based on an application of linear algebra adapted to the number theoretical needs.
Keywords
Cite
@article{arxiv.2011.09807,
title = {Congruence Subgroups and Orthogonal Groups},
author = {Adrian Hauffe-Waschbüsch and Aloys Krieg},
journal= {arXiv preprint arXiv:2011.09807},
year = {2021}
}