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

Proceedings of the American Mathematical Society, vol. 150, pp. 2357–2365

Abstract

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

Authors 2

1. Aloys Krieg Aachen Lehrstuhl A für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl A für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany

2. Felix Schaps Aachen Lehrstuhl A für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl A für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany