Non-restricted representations of contact and special contact Lie superalgebras of odd type

Let $\mathfrak{g}$ be a contact Lie superalgebra of odd type or special contact Lie superalgebra of odd type over an algebraically closed field of characteristic $p>3$. In this paper we study non-restricted representations of $\mathfrak{g}$. By using induced Kac modules, we characterize all simple $\mathfrak{g}$-modules with nonsingular or $\mathrm{\Delta }$-invertible $p$-characters. We also obtain all simple $\mathfrak{g}$-modules with regular semisimple $p$-characters.