Point Spectrum of the Dirac Operator on Noncompact Symmetric Spaces

摘要

In this note, the authors consider the Dirac Operator D on a Riemannian symmetric211u001espace M of noncompact type. Using represenation theory, the authors show that D 211u001ehas point spectrum if the A-genus of its compact dual does not vanish. In this 211u001ecase, if M is irreducible then M = U(p,q)/U(p) x U(q) with p + q odd, and 211u001eSpec(sup p)(D) + (0).