Representations of Lie superalgebras with fusion flags

We study the category of finite–dimensional representations for a basic classical Lie superalgebra $\text{Lg}={\text{Lg}}_0\oplus {\text{Lg}}_1$. For the ortho–symplectic Lie superalgebra $\text{Lg}=\mathfrak{o}\mathfrak{s}\mathfrak{p}(1,2n)$ we show that certain objects in that category admit a fusion flag, i.e. a sequence of graded ${\text{Lg}}_0[t]$–modules such that the successive quotients are isomorphic to fusion products. Among these objects we find fusion products of finite–dimensional irreducible $\text{Lg}$–modules, truncated Weyl modules and Demazure type modules. Moreover, we establish a presentation for these types of fusion products in terms of generators and relations of the enveloping algebra.