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Formally self adjointness for the Dirac operator on homogeneous spaces

1975

Introduction. In [5] , 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 be

doi:10.18910/7675
fatcat:kucv4kkvcna3hjre2ukedjgn3u