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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Eigenvalues and eigenspaces for the twisted Dirac operator over $ {\rm SU}(N,1)$ and $ {\rm Spin}(2N,1)$


Authors: Esther Galina and Jorge Vargas
Journal: Trans. Amer. Math. Soc. 345 (1994), 97-113
MSC: Primary 22E30; Secondary 22E45, 58G10
MathSciNet review: 1189792
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Abstract: 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 on $ {L^2}$-sections of certain homogeneous vector bundles over X. Using representation theory we obtain explicitly the eigenvalues of D and describe the eigenspaces in terms of the discrete series.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1189792-6
PII: S 0002-9947(1994)1189792-6
Keywords: Eigenvalues and eigenvectors for Dirac operator over $ SU(n,1)$ and over $ Spin(2n,1)$, discrete series, Blattner formula
Article copyright: © Copyright 1994 American Mathematical Society