New family of simple ${\mathfrak{gl}}_{2n}(\mathbb{C})$-modules

Abstract

We construct a new family of simple ${\mathfrak{gl}}_{2n}$-modules which depends on $n^2$ generic parameters. Each such module is isomorphic to the regular $U({\mathfrak{gl}}_n)$-module when restricted the ${\mathfrak{gl}}_n$-subalgebra naturally embedded into the top-left corner.

17 pages

References in corpus (3)

• Simple sl_{n+1}-module structures on U(h)
• $\mathcal{U}(\mathfrak{h})$-free modules and coherent families
• Irreducible Generic Gelfand-Tsetlin Modules of $\mathfrak{gl}(n)$

Cited by in corpus (3)

• Generalized Verma modules over $\fr{sl}_{n+2}$ induced from $\ca{U}(\fr{h}_n)$-free $\fr{sl}_{n+1}$-modules
• Non-weight representations of Cartan type S Lie algebras
• Simple $\mathfrak{sl}(V)$-modules which are free over an abelian subalgebra