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.

20 pages

References in corpus (3)

• Simple sl_{n+1}-module structures on U(h)
• $\mathcal{U}(\mathfrak{h})$-free modules and coherent families
• New family of simple ${\mathfrak{gl}}_{2n}(\mathbb{C})$-modules

Cited by in corpus (1)

• Module structure on $U(\mathfrak{h})$ for Kac-Moody algebras