Generalized Verma modules over $\fr{sl}_{n+2}$ induced from $\ca{U}(\fr{h}_n)$-free $\fr{sl}_{n+1}$-modules

Abstract: A class of generalized Verma modules over $\fr{sl}{n+2}$ is constructed from $\fr{sl}{n+1}$-modules which are $\uhn$-free modules of rank $1$. The necessary and sufficient conditions for these $\fr{sl}{n+2}$-modules to be simple are determined. This leads to a class of new simple $\fr{sl}{n+2}$-modules.