Patterns in Branching Rules for Irreducible Representations of SL2(k), for k a p-adic field

Building on prior work, we analyze the decomposition of the restriction of an irreducible representation of SL2(k), for k a p-adic field of odd residual characteristic, to a maximal compact subgroup K. The pattern of the decomposition varies between principal series and different supercuspidal representations, whereas the K-representations which occur in the "tail end" of these decompositions are precisely those occuring in the decomposition of depth-zero supercuspidal representations. Various applications are considered.