For manifolds with geodesic flow that is ergodic on the unit tangent bundle,the quantum ergodicity theorem implies that almost all Laplacian eigenfunctionsbecome equidistributed as the eigenvalue goes to infinity. For a locallysymmetric space with a universal cover that is a product of several upper halfplanes, the geodesic flow has constants of motion so it can not be ergodic. Itis, however, ergodic when restricted to the submanifolds defined by theseconstants. In accordance, we show that almost all eigenfunctions becomeequidistributed on these submanifolds.
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