UC Santa Cruz

Reeder, Yu, and Gross have studied a class of representations of p-adic groups which they call epipelagic – those which are just slightly deeper than the surface (depth zero). In this thesis, we systematically study the representations of minimal positive depth for groups of relative rank one over nonarchimedean local fields. These are the groups for which the (reduced) Bruhat-Tits building is a tree. For such groups, we give a simplified proof that all irreducible minimal-positive-depth supercuspidal representations arise via compact induction. Furthermore, for certain classes of these groups we explicitly describe the orbits that provide such induction data.