On Poisson transforms for spinors

Salem Ben Saïd, Abdelhamid Boussejra, Khalid Koufany

Research output: Contribution to journalArticlepeer-review

Abstract

Let (Formula presented) be a spinor representation of Spin (n) and let (σ, Vσ) be a spinor representation of Spin(n − 1) that occurs in the restriction (Formula presented). We consider the real hyperbolic space H n (R) as the rank one symmetric space Spin 0 (1, n)/ Spin (n) and the spinor bundle (Formula presented) as the homogeneous bundle Spin (Formula presented). In this paper we characterize eigenspinors of the algebra of invariant differential operators acting on 6H n (R) which can be written as the Poisson transform of L p -sections of the bundle Spin (Formula presented) over the boundary (Formula presented).

Original languageEnglish
Pages (from-to)771-792
Number of pages22
JournalTunisian Journal of Mathematics
Volume5
Issue number4
DOIs
Publication statusPublished - Nov 1 2023

Keywords

  • Poisson transform
  • Spin representation
  • Spinor bundle
  • real hyperbolic space

ASJC Scopus subject areas

  • General Mathematics

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