Spectra of compact locally symmetric manifolds of negative curvature

@article{Duistermaat1979SpectraOC,
  title={Spectra of compact locally symmetric manifolds of negative curvature},
  author={Johannes Jisse Duistermaat and J. A. C. Kolk and V. S. Varadarajan},
  journal={Inventiones mathematicae},
  year={1979},
  volume={54},
  pages={101}
}
Let S be a Riemannian symmetric space of noncompact type, and let G be the group of motions of S. Then the algebra L-~ of G-invariant differential operators on S is commutative, and its spectrum A(S) can be canonically identified with ~/w where ~ is a complex vector space with dimension equal to the rank of S, and to is a finite subgroup of G L ( ~ ) generated by reflexions. Let P be a discrete subgroup of G that acts freely on S and let X = E \ S . Then the members of 5~ may be regarded as… 
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