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

Let $\mathtt{G}$ 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 $\mathtt{G}$ to a maximal compact subgroup. Moreover, we analyse those features that distinguish this decomposition from the linear case.
 Keywords: local field, covering group, representation, Hilbert symbol, $\mathsf{K}$-type