A correspondence for the supercuspidal representations of $\overline {SL_2(F)}$, F p-adic

Following D. Manderscheid, we describe the supercuspidal representations of the n-fold metaplectic cover `(SL<sub>2</sub>(F))]\overline {SL_2(F)}, where F is a p-adic field with (p, 2n) = 1. We prove a "Frobenius formula" for the character of a supercuspidal representation of `(SL₂(F))]\overline {SL_2(F)}. Using this formula, we obtain a character relation between corresponding supercuspidal representations of `(SL₂(F))]\overline {SL_2(F)} and of SL₂(F)> in the case n = 2.