Maximal discrete subgroups of 𝑆𝑂⁺(2,𝑛+2)

Abstract

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