Categorification of Verma modules and indecomposable projective modules in the category ${\mathcal{I}}_{\mathfrak{g}}({\mathfrak{s}\mathfrak{l}}_2)$ for ${\mathfrak{s}\mathfrak{l}}_2$

We categorify Verma and indecomposable projective modules in the category ${\mathcal{I}}_{\mathfrak{g}}({\mathfrak{s}\mathfrak{l}}_2)$ for ${\mathfrak{s}\mathfrak{l}}_2$ using a tensor product decomposition theorem of T. J. Enright and work of J. Chuang and R. Rouquier, A. Licata and A. Savage (Hecke algebras, finite general linear groups, and Heisenberg categorification) and M. Khovanov (Heisenberg algebra and a graphical calculus).