On Poisson transform for spinors

2022/08/24 by Salem Bensaïd, Bensaïd, Salem, Abdelhamid Boussejra +3
Mathematics · Physics and Astronomy · #15A66 #22E30 #43A85 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2208.11763

openalex publication_date 2022/08/24 · openalex created_date 2022/08/27 · openalex updated_date 2026/08/02

Abstract

Let (τ,V_τ) be a spinor representation of Spin(n) and let (σ,V_σ) be a spinor representation of Spin(n-1) that occurs in the restriction τ_{| Spin(n-1)}. We consider the real hyperbolic space Hⁿ(\mathbb R) as the rank one homogeneous space Spin₀(1,n)/Spin(n) and the spinor bundle ΣHⁿ(\mathbb R) over Hⁿ(\mathbb R) as the homogeneous bundle Spin₀(1,n)×_Spin(n) V_τ. Our aim is to characterize eigenspinors of the algebra of invariant differential operators acting on ΣHⁿ(\mathbb R) which can be written as the Poisson transform of L^p-sections of the bundle Spin(n)×_Spin(n-1) V_σ over the boundary S^n-1≃ Spin(n)/Spin(n-1) of Hⁿ(\mathbb R), for 1

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