Compact manifold of coherent states invariant by semisimple Lie groups
We study local equivalence of left-invariant metrics with the same curvature on Lie groups and of dimension three, when is unimodular and is non-unimodular.
We prove that the global geometric theta-lifting functor for the dual pair is compatible with the Whittaker functors, where is one of the pairs , or . That is, the composition of the theta-lifting functor from to with the Whittaker functor for is isomorphic to the Whittaker functor for .