Tits Buildings for Symplectic Groups

This page is a supplement to the paper Das Titsgebäude von Siegelschen Modulgruppen vom Geschlecht 2, by M. Friedland and G.K. Sankaran. That paper is in German, because the basis of it is the Hannover Diplomarbeit of the first author. There is a short summary of the results in English.

Below we illustrate the Tits buildings for some of the symplectic groups. The pictures are in PostScript and were generated using MetaPost.

The research illustrated here was partly funded by the British Council and the DAAD under the British-German Academic Research Collaboration Programme.

• Tits buildings for the paramodular group of type (1,t), t squarefree. The representation depends on a nontrivial divisor s of t (though the building itself does not). For practical reasons we do not allow t/s=2: the picture with s=2 is similar anyway.
  • t=10, s=2
  • t=14, s=2
  • t=15, s=3
  • t=15, s=5
  • t=21, s=3
  • t=21, s=7
  • t=30, s=2
  • t=30, s=3
  • t=30, s=5
  • t=30, s=6
  • t=30, s=10
• Tits buildings for the level-q paramodular group of type (1,p) with p, q prime and p odd. So far we have only drawn the case q=2 (it is independent of p).
• A tetrahedron, representing lines in projective 3-space over the field with 2 elements, which also decribes the Tits building for q=2.