Commutant algebra and harmonic polynomials of the Lie algebra of vector fields (Q1921924)

Let \(W_n\) be the Lie algebra of vector fields on a vector space \(V=K^n\) with polynomial coefficients, where \(K\) is a field of characteristic 0. The author determines the commutant algebra of \(W_n\) in the \(m\)-fold tensor product of its natural representation in the case \(m\leq n\). For \(m>n\), the author shows that the commutant algebra is of finite dimension by introducing a new kind of harmonic polynomial.