We study the elliptic Ruijsenaars models associated with arbitrary root systems, which are difference analogs of the Calogero–Moser model. We give a dense subspace in the space of square integrable functions invariant under the action of the Weyl group on a torus as a domain of its Hamiltonian and prove its essential self-adjointness by using perturbation theory. It is also clarified that these models consist of pure point spectrum.

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