ON THE EIGENFUNCTIONS OF THE DIRAC OPERATOR ON SPHERES AND REAL HYPERBOLIC SPACES

The eigenfunctions of the Dirac operator on spheres and real hyperboli c spaces of arbitrary dimension are computed by separating variables i n geodesic polar coordinates. These eigenfunctions are then used to de rive the heat kernel of the iterated Dirac operator on these spaces. T hey are then studied as cross sections of homogeneous vector bundles, and a group-theoretic derivation of the spinor spherical functions and heat kernel is given based on Harish-Chandra's formula for the radial part of the Casimir operator.