Irreducible representations of the Hamiltonian algebra H(2r; n)

Let L=H(2r;n) be a graded Lie algebra of Hamiltonian type in the Cartan type series over an algebraically closed field of characteristic p>2. In the generalized restricted Lie algebra setup, any irreducible representation of L corresponds uniquely to a (generalized) p-character χ. When the height of χ is no more than min {p ⁿⁱ - p ^ni-1|i=1,2,...,2r} - 2, the corresponding irreducible representations are proved to be induced from irreducible representations of the distinguished maximal subalgebra L ₀ with the aid of an analogy of Skryabin's category black-letter capital C sign for the generalized Jacobson-Witt algebras and modulo finitely many exceptional cases. Since the exceptional simple modules have been classified, we can then give a full description of the irreducible representations with p-characters of height below this number.