Pictures of compact Lie groups (after Serre)

Abstract

We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp($2n$), the picture generated by the method is connected with abelian varieties over a number field or a finite field. We follow the procedure to produce pictures for the three simply connected simple groups of rank 2. The pictures for two of these have previously been discussed in the literature in a different setting. The remaining one, type $G_2$, has the most complicated picture.