Shen-Larsson modules over the lie algebras of divergence zero vector fields on ℂ n

Let n≥2 be an integer, Sn be the Lie algebra of vector fields on Cn with zero divergence, and Dn be the Weyl algebra over the polynomial algebra An=C[t1,t2,⋯,tn]. In this paper, we study the simplicity of the Shen-Larsson Sn-module F(P,M), where P is a simple Dn-module and M is a simple sln-module. We obtain the necessary and sufficient conditions for F(P,M) to be an irreducible module, and determine all simple subquotients of F(P,M) when it is reducible.