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Let $\widetilde{G}$ be the $n$-fold covering group of the special lineargroup of degree two, over a non-Archimedean local field. We determine thedecomposition into irreducibles of the restriction of the principal seriesrepresentations of $\widetilde{G}$ to a maximal compact subgroup of$\widetilde{G}$.

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