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Given an algebraically closed field $F$ of characteristic 0 and an $F$-vectorspace $V$, let $L(V)=V\oplus\Lambda^2(V)$ denote the free 2-step nilpotent Liealgebra associated to $V$. In this paper, we classify all uniserialrepresentations of the solvable Lie algebra $\mathfrak g=\langlex\rangle\ltimes L(V)$, where $x$ acts on $V$ via an arbitrary invertible Jordanblock.

Free 2-step nilpotent Lie algebras and indecomposable modules