Geodesic
Intermediate Lie algebras and their finite finite-dimensional representations
Izvestiya. Mathematics , Tome 43 (1994) no. 3, pp. 559-579

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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. 
@article{IM2_1994_43_3_a8,
     author = {V. V. Shtepin},
     title = {Intermediate {Lie} algebras and their finite finite-dimensional representations},
     journal = {Izvestiya. Mathematics },
     pages = {559--579},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1994_43_3_a8/}
}
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V. V. Shtepin. Intermediate Lie algebras and their finite finite-dimensional representations. Izvestiya. Mathematics , Tome 43 (1994) no. 3, pp. 559-579. http://geodesic.mathdoc.fr/item/IM2_1994_43_3_a8/