Irreducible jet modules for the vector field Lie algebra on S1×C

For a commutative algebra A over C, denote g=Der(A). module the smash product A#U(g) is called jet g-module, where U(g) universal enveloping of g. In present paper, we study modules in case A=C[t1±1,t2]. We show that A#U(g)≅D⊗U(L), D Weyl C[t1±1,t2,∂∂t1,∂∂t2], and L Lie subalgebra corresponding to Using isomorphism θ:L→m1,0Δ, m1,0Δ vector fields vanishing at point (1, 0), any irreducible finite dimensional L-module isomorphic an gl2-module. As application, give tensor realizations g with uniformly bounded weight spaces.