We prove, using a technique developed for
$GL(n)$ in Howe and Moy [H],
a bijection between generalized Hecke
algebras of $G=SL(2,F)$ over a $p$-adic field
and those of its $n$-fold metaplectic cover $\overline{G}$.
This result implies that
there is a canonical correspondence
between irreducible admissible representations of $G$ and
genuine irreducible admissible representations of $\overline{G}$
of ``sufficiently large level" (depending on $n,p$).
[H] R. Howe (with the collaboration of A. Moy),
{\it Harish-Chandra homomorphisms for p-adic groups},
CBMS Regional Conference Series in Mathematics,
No.~59, Amer. Math. Soc., Providence, 1985, MR 87h:22023.