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We generalize the methods of Moy-Prasad, in order to define and study thegenuine depth zero representations of some nonlinear covers of reductive groupsover $p$-adic local fields. In particular, we construct all depth zerosupercuspidal representations of the metaplectic group $Mp_{2n}$ over a$p$-adic field of odd residue characteristic.

Depth Zero Representations of Nonlinear Covers of $p$-adic Groups