Branching Rules for $n$-fold Covering Groups of ${\mathrm{S}\mathrm{L}}_2$ over a Non-Archimedean Local Field

Let $\tilde{G}$ be the $n$-fold covering group of the special linear group of degree two, over a non-Archimedean local field. We determine the decomposition into irreducibles of the restriction of the principal series representations of $\tilde{G}$ to a maximal compact subgroup of $\tilde{G}$.