10/26/2006

Alireza Salehi Golsefidi
Princeton University

Discrete transitive actions on the vertices of Bruhat-Tits buildings

In this work, joint with A. Mohammadi, we try to classify  all the discrete transitive actions on the vertices of a Bruhat-Tits Building over a local field of characteristic zero. There are lots of such actions in the case of Bruhat-Tits tree, i.e. rank one case. However these actions are rare in the higher rank; in fact,  only a few are known in dimension at most five. In this talk, I will explain a recent theorem stating that there are no such actions in dimension larger than 8. In the proof we will work with the arithmetic structure of such actions and make use of Tamagawa numbers and Prasad's work.