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Introduction. In  , Wolf proved that the Dirac operator is essentially self adojoint over a Riemannian spin manifold M and he used it to give explicit realization of unitary representations of Lie groups. Let K be a Lie group and a a Lie group homomorphism of K into SO(n) which factors through Spin (ή). He defined the Dirac operator on spinors with values in a certain vector bundle under the assumption that the Riemannian connection on the oriented orthonormal frame bundle P over M can bedoi:10.18910/7675 fatcat:kucv4kkvcna3hjre2ukedjgn3u