In this paper we first construct natural filtrations on the full theta lifts
for any real reductive dual pairs. We will use these filtrations to calculate
the associated cycles and therefore the associated varieties of Harish-Chandra
modules of the indefinite orthogonal groups which are theta lifts of unitary
lowest weight modules of the metaplectic double covers of the real symplectic
groups. We will show that some of these representations are special unipotent
and satisfy a K-type formula in a conjecture of Vogan.Comment: The current version is a major revision of the first draft where we
incorporate ideas from a recent paper arXiv:1302.1031. We bypass the K-types
and asymptote calculations, and give more geometric and conceptual proof