Associated cycles of local theta lifts of unitary characters and unitary   lowest weight modules
  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. 
Hung Yean Loke, Jia-jun Ma, U-Liang Tang
math.RT