On the self-adjointness of certain reduced Laplace-Beltrami operators (Q1025365)

The paper studies self-adjointness of the reduced Hamiltonian operators arising from the Laplace-Beltrami operator of a complete Riemannian manifold through quantum Hamiltonian reduction based on a compact isometry group. A simple sufficient condition is given which guarantees the inheritance of essential self-adjointness onto a certain class of restricted operators and allows to conclude self-adjointness of the reduced Laplace-Beltrami operators in a concise way. As a consequence, the self-adjointness of spin Calogero-Sutherland type reductions of ``free'' Hamiltonians under polar actions of compact Lie groups follows immediately.