• Corpus ID: 118100546

Duflo's conjecture for the branching to the Iwasawa $AN$-subgroup

@article{Liu2012DuflosCF,
  title={Duflo's conjecture for the branching to the Iwasawa \$AN\$-subgroup},
  author={Gang Liu},
  journal={arXiv: Representation Theory},
  year={2012}
}
  • Gang Liu
  • Published 20 July 2012
  • Mathematics
  • arXiv: Representation Theory
The purpose of this paper is to prove Duflo's conjecture for $(G,\pi, AN)$ where $G$ is a simple Lie group of Hermitian type and $\pi$ 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 $\mathcal{O}$ is holomorphic if and only if $\text{p}(\mathcal{O… 
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