Supercuspidal representations and preservation principle of theta correspondence

The preservation principle of the local theta correspondence predicts the existence of a chain of irreducible supercuspidal representations of p-adic classical groups. In this paper, we give an explicit characterization of the chain starting from an irreducible supercuspidal representations of a unitary group of one variable or an orthogonal group of two variables. In particular, we define the Lusztig-like correspondence of generic cuspidal data for p-adic groups and establish its relation with local theta correspondence of supercuspidal representations for p-adic dual pairs.