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

2012/07/27 by Hung Yean Loke, Loke, Hung Yean, Jia-Jun Ma +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1207.6451

openalex publication_date 2012/07/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Related

• On two geometric theta lifts
• The explicit theta correspondence for reductive dual pairs (Sp(p,q),O^*(4))
• Theta correspondence for symplectic-orthogonal and metaplectic-orthogonal p-adic dual pairs
• Theta lifting for discrete series representations of real unitary groups
• Theta liftings of non-generic representations on double covers of orthogonal groups