EIGENVALUES AND EIGENSPACES FOR THE TWISTED DIRAC OPERATOR OVER SU(N,1) AND SPIN(2N, 1)

Let X be a symmetric space of noncompact type whose isometry group is either SU(n, 1) or Spin(2n, 1). Then the Dirac operator D is defined o n L(2)-sections of certain homogeneous vector bundles over X. Using re presentation theory we obtain explicitly the eigenvalues of D and desc ribe the eigenspaces in terms of the discrete series.