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On the algebraic structure of the Lie algebra of vector fields on the line

A. I. Molev


Abstract: 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.

UDC: 512.5

MSC: Primary 17B65; Secondary 20C30

Received: 27.08.1986

 English version: Mathematics of the USSR-Sbornik, 1989, 62:1, 83–94

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