turkmath.org

Gross, Reeder, and Yu have studied a class of supercuspidal representations of p-adic groups which they call epipelagic — those slightly deeper than the surface (depth zero). In this talk, we will systematically study the epipelagic representations of minimal positive depth for p-adic groups of semisimple rank one. These are the groups for which the Bruhat-Tits building is a tree. For such groups, we provide a simplified proof that all minimal positive depth supercuspidals arise via compact induction, and we will explicitly describe the orbits that provide such induction data.