UC Santa Cruz

The aim of this thesis is to describe the principal series representations of SL(2,p), together with the character tables of some of its subgroups. We describe all irreducible characters and conjugacy classes of a Borel subgroup B < SL(2,p), the standard torus T < SL(2,p), and the unipotent subgroup U < B. We go on to completely describe the principal series of SL(2,p), those representations induced from characters of B.