The purpose for this short note is to describe the space of harmonic spinors on hyperbolic n-space Hn
. This is a natural continuation of the study of harmonic functions on Hn
in [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms on Hn
were considered. The connection between invariant differential equations on a Riemannian semisimple symmetric space G/K and homological aspects of the representation theory of G, as exemplified in (8) below, does not seem to have been previously mentioned. This note is divided into three main parts respectively dedicated to the statement of the results, some reminders, and the proofs. I thank the referee for having suggested various improvements.