Holomorphically Induced Representations of Some Solvable Lie Groups

We study holomorphically induced representations ρ of Lie groups G=exp g from weak polarizations h at f∈g*. When G is a connected and simply connected Lie group whose Lie algebra is a normal j-algebra, we obtain a sufficient condition for non-vanishing of ρ and the decomposition of ρ into irreducible representations under the assumption that the coadjoint G-orbit Gċf is open and h is a positive weak polarization at f.