On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0

Abstract

Let $H(2,1;\underline{t})$ be Hamiltonian superalgebras over $\mathbb{F}$, an algebraically closed field of prime characteristic $p>3$, which are non-restricted simple Lie superalgebras, generally. In this paper, we study generalized $\chi$-reduced simple modules over $H(2,1;\underline{t})$. We proved that all generalized $\chi$-reduced Kac modules of $H(2,1;\underline{t})$ are simple with $p$-characters $\chi$ of height 0. Additionally, the isomorphism classes of these simple $H(2,1;\underline{t})$-modules are classified and their dimensions are determined.