Geodesic
Irreducible representations of~infinite-dimensional Lie algebras of Cartan type
Izvestiya. Mathematics , Tome 8 (1974) no. 4, pp. 836-866.

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In this paper the irreducible representations of infinite-dimensional filtered Lie algebras are studied. The concept of the height of a representation is introduced, and it is proved that the representations of height greater than one of the Lie algebras $\mathbf W_n$, $\mathbf S_n$, $\mathbf H_n$ and $\mathbf K_n$ are induced. The representations of height one of the algebras $\mathbf W_n$ are also described. 
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     author = {A. N. Rudakov},
     title = {Irreducible representations of~infinite-dimensional {Lie} algebras of {Cartan} type},
     journal = {Izvestiya. Mathematics },
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A. N. Rudakov. Irreducible representations of~infinite-dimensional Lie algebras of Cartan type. Izvestiya. Mathematics , Tome 8 (1974) no. 4, pp. 836-866. http://geodesic.mathdoc.fr/item/IM2_1974_8_4_a3/

[1] Singer I. M., Sternberg S., “The infinite groups of Lie and Cartan”, J. Analise Math., 15 (1965), 1–114 | DOI | MR | Zbl