• 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… 

References

SHOWING 1-10 OF 15 REFERENCES
Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups III. Restriction of Harish-Chandra modules and associated varieties
Abstract. Let H⊂G be real reductive Lie groups and π an irreducible unitary representation of G. We introduce an algebraic formulation (discretely decomposable restriction) to single out the nice
Geometric quantization and multiplicities of group representations
The Heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum-mechanical particle. This can be rephrased as follows: the smallest
Discrete decomposability of the restriction of A_q(λ)with respect to reductive subgroups II-micro-local analysis and asymptotic K-support
Let G' c G be real reductive Lie groups. This paper offers a criterion on the triplet (G, G', ir) that the irreducible unitary representation ir of G splits into a discrete sum of irreducible unitary
Branching laws for square integrable representations
In this note, we study square integrable representations of a real reductive Lie group with admissible restriction to some reductive subgroup. We give a simple condition which insures admissibility
Causal symmetric spaces : geometry and harmonic analysis
Symmetric spaces: basic structure theory, dual symmetric spaces, the module structure of q, a-subspaces, the hyperboloids. Causal orientations: covex cones and their auto-morphisms, causal
Lie groups beyond an introduction
Preface to the Second Edition Preface to the First Edition List of Figures Prerequisites by Chapter Standard Notation Introduction: Closed Linear Groups Lie Algebras and Lie Groups Complex Semisimple
Restriction des séries discrètes de SU(2,1) à un sous-groupe exponentiel maximal et à un sous-groupe de Borel
Dans cette these, nous explicitons la decomposition en irreductibles de la restriction d’une serie discrete du groupe SU(2,1) a un sous-groupe exponentiel maximal et a un sous-groupe de Borel et nous
Oxford University Press in Africa, 1927â80
...
...