The point spectrum of the Dirac operator on noncompact symmetric spaces

Abstract

In this note, we consider the Dirac operator $D$ on a Riemannian symmetric space $M$ of noncompact type. Using representation theory we show that $D$ has point spectrum iff the $\hat{A}$-genus of its compact dual does not vanish. In this case, if $M$ is irreducible then $M=U(p,q)/U(p)\times U(q)$ with $p+q$ odd, and $Spe{c}_p(D)=\{0\}$.

arXiv commentamstex, 8 pages

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