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In the case of complex symplectic and orthogonal groups, we find$(\mathfrak{g}, K)-$modules with the property that their $K-$structure matchesthe structure of regular functions on the closures of nilpotent orbits. Thisestablishes a version of the Orbit Method of Kirrilov-Kostant-Souriau asproposed by Vogan. In the process we give another proof of the classificationof nilpotent orbits with normal closure in the Lie algebra of a classical groupfirst established by Kraft-Procesi.

Admissible modules and normality of classical nilpotent orbits I