Geodesic
On the algebraic structure of the Lie algebra of vector fields on the line
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 83-94

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The author obtains a description of the structure of a representation of the symmetric group $S_n$ in the space of $n$-linear elements of the variety of Lie algebras generated by the Lie algebra of vector fields on the line. It is proved that this space, as an $S_n$-module, is isomorphic to the space of homogeneous harmonic polynomials of degree $n-1$ in $n$ variables. Bibliography: 16 titles. 
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     author = {A. I. Molev},
     title = {On the algebraic structure of the {Lie} algebra of vector fields on the line},
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A. I. Molev. On the algebraic structure of the Lie algebra of vector fields on the line. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 83-94. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a4/