The point spectrum of the Dirac operator on noncompact symmetric spaces

Details The point spectrum of the Dirac operator on noncompact symmetric spaces The point spectrum of the Dirac operator on noncompact symmetric spaces

1999-03-30

arxiv.org/abs/math/9903177v1

Proc. Amer. Math. Soc. 130 (2002), 915-923

Mathematics

Differential Geometry

amstex, 8 pages

Scientific paper

10.1090/S0002-9939-01-06158-5

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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