Supercuspidal representations and preservation principle of theta correspondence

Abstract

<jats:title>Abstract</jats:title> <jats:p>The preservation principle of the local theta correspondence predicts the existence of a chain of irreducible supercuspidal representations of <jats:italic>p</jats:italic>-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 <jats:italic>p</jats:italic>-adic groups and establish its relation with local theta correspondence of supercuspidal representations for <jats:italic>p</jats:italic>-adic dual pairs.</jats:p>