Intermediate Lie algebras and their finite finite-dimensional representations

A method is exhibited for separating multiple points of the spectrum in the reductions $A_n\downarrow A_{n-1}$ and $C_n\downarrow C_{n-1}$ by introducing nonsemisimple intermediate subalgebras. The category of modules over these intermediate subalgebras is examined; the modules play the role of modules with highest weight.