Branching rules for the restriction of regular representations of GL ₂ (o/℘ r ) to SL ₂ (o/℘ r )

Let o be a compact discrete valuation ring with maximal ideal ℘ such that the finite residue field o/℘ has characteristic p. For r≥2 and p=2, we obtain the branching rules for the restriction of a regular representation of GL2(o/℘r) to SL2(o/℘r). These results have different behavior than that of the known case of p≠2.