MULTIPLICITY FORMULA FOR RESTRICTION OF REPRESENTATIONS OF (GL(2))over-tilde(F) TO (SL2)over-tilde(F)

In this note we prove a certain multiplicity formula regarding the restriction of an irreducible admissible genuine representation of a 2-fold cover (GL(2)) over tilde (F) of CL2(F) to the 2-fold cover (SL2) over tilde (F) of SL2(F), and find in particular that this multiplicity may not be one, a result that was recently observed for certain principal series representations in the work of Szpruch (2013). The proofs follow the standard path via Waldspurger's analysis of theta correspondence between (SL2) over tilde (F) and PGL(2)(F)