On Poisson transform for spinors

Let \((\tau,V_\tau)\) be a spinor representation of \(\mathrm{Spin}(n)\) and let \((\sigma,V_\sigma)\) be a spinor representation of \(\mathrm{Spin}(n-1)\) that occurs in the restriction \(\tau_{\mid \mathrm{Spin}(n-1)}\). We consider the real hyperbolic space \(H^n(\mathbb R)\) as the rank one homo...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Salem Bensaïd, Boussejra, Abdelhamid, Koufany, Khalid
Format: Article
Language:English
Subjects:
Differential equations
Hyperbolic coordinates
Operators (mathematics)
Representations
Online Access:Get full text
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Summary:Let \((\tau,V_\tau)\) be a spinor representation of \(\mathrm{Spin}(n)\) and let \((\sigma,V_\sigma)\) be a spinor representation of \(\mathrm{Spin}(n-1)\) that occurs in the restriction \(\tau_{\mid \mathrm{Spin}(n-1)}\). We consider the real hyperbolic space \(H^n(\mathbb R)\) as the rank one homogeneous space \(\mathrm{Spin}_0(1,n)/\mathrm{Spin}(n)\) and the spinor bundle \(\Sigma H^n(\mathbb R)\) over \(H^n(\mathbb R)\) as the homogeneous bundle \(\mathrm{Spin}_0(1,n)\times_{\mathrm{Spin}(n)} V_\tau\). Our aim is to characterize eigenspinors of the algebra of invariant differential operators acting on \(\Sigma H^n(\mathbb R)\) which can be written as the Poisson transform of \(L^p\)-sections of the bundle \(\mathrm{Spin}(n)\times_{\mathrm{Spin}(n-1)} V_\sigma\) over the boundary \(S^{n-1}\simeq \mathrm{Spin}(n)/\mathrm{Spin}(n-1)\) of \(H^n(\mathbb R)\), for \(1
ISSN:2331-8422