Abstract
Let S be a completely solvable, ad-algebraic connected and simply connected Lie group with Lie algebra J . Let λ ϵ J ∗ and let P be a totally complex, metric polarization for λ which satisfies the complex Pukanszky condition. In this work we prove the non-triviality and irreducibility of the harmonically induced representation corresponding to the given data. For these results to hold, it is necessary to replace the invariant metric on the coadjoint orbit by a semi-invariant metric. It is proven that these results also have applications to the study of homogeneous domains in C n .
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