# Associated cycles of local theta lifts of unitary characters and unitary lowest weight modules

@article{Loke2012AssociatedCO, title={Associated cycles of local theta lifts of unitary characters and unitary lowest weight modules}, author={Hung Yean Loke and Jia-jun Ma and U-Liang Tang}, journal={arXiv: Representation Theory}, year={2012} }

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…

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### Invariants and $K$-spectrums of local theta lifts

- MathematicsCompositio Mathematica
- 2014

Abstract Let $(G,G^{\prime })$ be a type I irreducible reductive dual pair in Sp$(W_{\mathbb{R}})$. We assume that $(G,G^{\prime })$ is in the stable range where $G$ is the smaller member. Let $K$…

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