Abstract
In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs (U 1 (F),U 1 (F)), (U 1 (F),U 1,1 (F)), (U 1 (F),U 2 (F)), and (U 1 (F),U 1,2 (F)) of unitary groups over a nonarchimedean local field F of odd residue characteristic. ©2005 American Mathematical Society.