Normalizers of Congruence Groups in $SL_{2}(\mathbb{R})$ and Automorphisms of Lattices

Shaul Zemel

doi:10.1142/S1793042117500701

paper

Normalizers of Congruence Groups in $S L_{2} (R)$ and Automorphisms of Lattices

arXiv:1512.07547 · doi:10.1142/S1793042117500701

Abstract

We determine the normalizer in $S L_{2} (R)$ of several families of congruence subgroups of $S L_{2} (Z)$ . In addition, we show how these tools can be used to evaluate the groups of automorphisms and the discriminant kernels of a large family of isotropic lattices of signature (2,1).

26 pages, exposition smoothened, added required assumption of characteristic 0 in Proposition 4.6

Normalizers of Congruence Groups in SL2​(R) and Automorphisms of Lattices

Abstract

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Normalizers of Congruence Groups in $S L_{2} (R)$ and Automorphisms of Lattices