Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

Abstract

We prove that the tensor product of a simple and a finite dimensional ${\mathfrak{sl}}_n$-module has finite type socle. This is applied to reduce classification of simple $\mathfrak{q}(n)$-supermodules to that of simple ${\mathfrak{sl}}_n$-modules. Rough structure of simple $\mathfrak{q}(n)$-supermodules, considered as ${\mathfrak{sl}}_n$-modules, is described in terms of the combinatorics of category $\mathcal{O}$.

Cited by in corpus (2)

• Parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for periplectic Lie superalgebras $\mathfrak{pe}(n)$
• Some homological properties of category $\mathcal{O}$ for Lie superalgebras