Abstract

Let $(\tau ,V_{\tau })$ be a spinor representation of $\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n)$ and let $(\sigma ,V_{\sigma })$ be a spinor representation of $\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n-1)$ that occurs in the restriction ${\tau }_{|\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n-1)}$.

We consider the real hyperbolic space $H^n(ℝ)$ as the rank one symmetric space ${\mathrm{Spin}<!--FUNCTION\; APPLICATION-->}_0(1,n)∕\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n)$ and the spinor bundle $\mathrm{\Sigma }{H}^n(ℝ)$ over $H^n(ℝ)$ as the homogeneous bundle ${\mathrm{Spin}<!--FUNCTION\; APPLICATION-->}_0(1,n){\times }_{\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n)}{V}_{\tau }$.

In this paper we characterize eigenspinors of the algebra of invariant differential operators acting on $\mathrm{\Sigma }{H}^n(ℝ)$ which can be written as the Poisson transform of $L^p$-sections of the bundle $\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n){\times }_{\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n-1)}{V}_{\sigma }$ over the boundary $S^{n-1}\simeq \mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n)∕\mathrm{Spin}<!--FUNCTION\; APPLICATION-->(n-1)$ of $H^n(ℝ)$, for $1<p<\infty$.

Keywords

Mathematical Subject Classification

Milestones

Authors