Restricted Irreducible Representations for the Non-graded Hamiltonian $H(2;(1,1);\mathrm{\Phi }(1))$

We classify the simple restricted modules for the minimal $p$-envelope of the non-graded, non-restricted Hamiltonian Lie algebra $H(2;(1,1);\mathrm{\Phi }(1))$ over an algebraically closed field $k$ of characteristic $p\ge 5$. We also give the restrictions of these modules to a subalgebra isomorphic to the first Witt Algebra, a result stated in [S. Herpel and D. Stewart, \emph{Selecta Mathematica} 22:2 (2016) 765–799] with an incomplete proof.