The subsingular-vector factor conjecture for twisted Heisenberg–Virasoro modules

Let $V(c,\frac{1-r}{2},0)$ be the module in question, let $J^{\prime}(c,\frac{1-r}{2},0)$ denote the specified submodule, and let $u$ be a subsingular vector in $V(c,\frac{1-r}{2},0)$. Subsingular-vector factor conjecture. The factor $L_{-k}$ for every $k>1$ does not occur in $u$. In particular,

$$W_{0}u,W_{-1}u\in J^{\prime}(c,\frac{1-r}{2},0).$$

This conjecture describes a restriction on the form of subsingular vectors and implies that the indicated actions of $W_0$ and $W_{-1}$ lie in the specified submodule. Its resolution is not given in the supplied text.