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Register a new userThe point spectrum of the Dirac operator on noncompact symmetric spaces
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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 $Spec_p(D) = {0}$.
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