Construction of simple non-weight sl(2)-modules of arbitrary rank

Abstract

We study simple non-weight $\mathfrak{sl}(2)$-modules which are finitely generated as $\mathbb{C}[z]$-modules. We show that they are described in terms of semilinear endomorphisms and prove that the Smith type induces a stratification on the set of these $\mathfrak{sl}(2)$-modules, providing thus new invariants. Moreover, we show that there is a notion of duality for these type of $\mathfrak{sl}(2)$-modules. Finally, we show that there are simple non-weight $\mathfrak{sl}(2)$-modules of arbitrary rank by constructing a whole new family of them.

References in corpus (2)

• Simple sl_{n+1}-module structures on U(h)
• Extending Representations of sl(2) to Witt and Virasoro algebras

Cited by in corpus (1)

• A family of non-weight modules over the super-Virasoro algebras