THE SPECTRUM OF THE DIRAC OPERATOR ON THE HYPERBOLIC SPACE

We represent the real hyperbolic space H(n) as the rank one homogeneous space Spin (1, n)/Spin (n) and the spinor bundle S of H as the homogeneous bundle Spin (1, n) x Spin (n)V(DELTA)where V(DELTA) is the spinor representation space of Spin (n). The representation theoretic decomposition of L2(H, S) combined with the PARTHASARATHY formula for the DIRAC operator D yields the spectral representation of D2.