Representations of Hamiltonian Lie algebras

We consider the Shen-Larsson functor from the category of modules for the symplectic Lie algebra to the category of modules for the Hamiltonian Lie algebra and show that it preserves the irreducibility except in the finite number of cases. The obtained irreducible modules for the Hamiltonian Lie algebra are cuspidal, whose weight multiplicities equal the dimension of the corresponding module of the symplectic Lie algebra. This extends well-known results for other Cartan type Lie algebras to the Hamiltonian case.