Maximal Discrete Subgroups of $S{O}^{+}(2,n+2)$

Abstract

We characterize the maximal discrete subgroups of $S{O}^{+}(2,n+2)$, which contain the discriminant kernel of an even lattice, which contains two hyperbolic planes over $\mathbb{Z}$. They coincide with the normalizers in $S{O}^{+}(2,n+2)$ and are given by the group of all integral matrices inside $S{O}^{+}(2,n+2)$, whenever the underlying lattice is maximal even. Finally we deal with the irreducible root lattices as examples.

References in corpus (6)

• On some free algebras of orthogonal modular forms
• The classification of free algebras of orthogonal modular forms
• Congruence Subgroups and Orthogonal Groups
• Projective spaces as orthogonal modular varieties
• Simple lattices and free algebras of modular forms
• Reflective modular forms on lattices of prime level