2012/07/20 by Gang Liu, Liu, Gang
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1207.5071
arxiv created 2012/07/20 · openalex publication_date 2012/07/20 · arxiv updated 2012/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to prove Duflo's conjecture for (G,π, AN) where G is a simple Lie group of Hermitian type and π is a discrete series of G and AN is the maximal exponential solvable subgroup for an Iwasawa decomposition G=KAN. This is essentially reduced from the following general theorem we prove in this paper: let G be a connected semisimple Lie group . Then a strongly elliptic G-coadjoint orbit O is holomorphic if and only if p(O) is an open AN-coadjoint orbit, where p : \mathfrakg^* \longrightarrow (\mathfraka⊕\mathfrakn)^* is the natural projection.