First order differential operators on a locally symmetric space (Q1587534)

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.