反德西特空间 SOe(2,2)/SOe(2,1)$\mathop {rm {SO_e}}(2,2)/\mathop {\rm {SO_e}}(2,1)$ 的达朗贝尔共振

Pub Date : 2024-06-30 DOI:10.1002/mana.202300212

Simon Roby

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引用次数: 0

摘要

我们考虑了伪黎曼三维反德西特空间上的达朗贝尔函数作用。我们确定了这一算子的共振。每个共振都可以关联一个残差表示。我们通过朗兰兹参数对这些表示给出了明确的描述。

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Resonances of the d'Alembertian on the anti-de Sitter space SO e ( 2 , 2 ) / SO e ( 2 , 1 ) $\mathop {\rm {SO_e}}(2,2)/\mathop {\rm {SO_e}}(2,1)$

We consider the action of the d'Alembertian on functions on the pseudo-Riemannian three-dimensional anti-de Sitter space. We determine the resonances of this operator. With each resonance one can associate a residue representation. We give an explicit description of these representations via Langlands parameters.

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