The Bruhat-Tits building of a p-adic Chevalley group and an application to representation theory

This thesis is concerned with the structure theory of generalized Levi subgroups G of simply-connected Chevalley groups defined over a finite extension of a p-adic field. We present a geometric parameterization of this structure known as the Bruhat-Tits building B(G). The building facilitates visualizing and reasoning about the structure ofG, and therefore has applications to all things related to such groups. We present Moy and Prasad’s classification of depth-zero super-cuspidal representations of G using the building. Such representations are obtained by induction from cuspidal representations of finite Chevalley groups — this is therefore an important connection between p-adic representation theory and the representation theory of finite groups of Lie type.