First order differential operators on a locally symmetric space. (English) Zbl 1027.58027

The authors consider the quotient \(\Gamma\setminus M\) of a symmetric space \(M=G/H\) such that \(M\) is a spin manifold and a discrete subgroup \(\Gamma\subset G\). They prove that any invariant elliptic operator of first order on \(\Gamma\setminus M\) is a twisted Dirac operator. Moreover, they give conditions for the equivariance of the spectral symmetry of such operators.


58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C35 Differential geometry of symmetric spaces
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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