Graded representations of current Lie superalgebra sl(1|2)[t]

In this paper, we study finite-dimensional graded representations of the current Lie superalgebra $\mathrm{sl}\left(1\right|2\left)\right[t]$. We define the notion of super POPs, a combinatorial tool to provide another parametrization of the basis of the local Weyl module given by Brito, Calixto and Macedo. We derive the graded character formula of the local Weyl module for $\mathrm{sl}\left(1\right|2\left)\right[t]$. Furthermore, we construct a short exact sequence of Chari-Venkatesh modules for $\mathrm{sl}\left(1\right|2\left)\right[t]$. As a consequence, we prove that Chari-Venkatesh modules are isomorphic to the fusion product of generalized Kac modules.