Simple sl_{n+1}-module structures on U(h)

Abstract

We study the category M consisting of U(sl_{n+1})-modules whose restriction to U(h) is free of rank 1, in particular we classify isomorphism classes of objects in M and determine their submodule structure. This leads to new sl_{n+1}-modules. For n=1 we also find the central characters and derive an explicit formula for taking tensor product with a simple finite dimensional module.

Cited by in corpus (31)

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• A family of non-weight modules over the super-Virasoro algebras
• Non-weight modules over algebras related to the Virasoro algebra
• Non-weight modules over the affine-Virasoro algebra of type $A_1$
• New family of simple ${\mathfrak{gl}}_{2n}(\mathbb{C})$-modules
• Irreducible modules over Witt algebras ${\mathcal{W}}_n$ and over ${\mathfrak{sl}}_{n+1}(\mathbb{C})$
• $\W_n^+$- and $W_n$-module structures on $U(h)$
• Simple Witt modules that are finitely generated over the cartan subalgebra
• A class of non-weight modules over the Schrödinger-Virasoro algebras
• Module structure on $U(\mathfrak{h})$ for Kac-Moody algebras
• $U(\fh)$-free modules over the Block algebra $\BB(q)$
• Regularity of quasigeodesics characterises hyperbolicity
• Construction of simple non-weight sl(2)-modules of arbitrary rank
• Irreducible weight modules over Witt algebras with infinite dimensional weight spaces
• A family of simple non-weight modules over the twisted $N=2$ superconformal algebra
• On non-weight representations of the $N=2$ superconformal algebras
• Generalized Verma modules over $\fr{sl}_{n+2}$ induced from $\ca{U}(\fr{h}_n)$-free $\fr{sl}_{n+1}$-modules
• Simple restricted modules over the Heisenberg-Virasoro algebra as VOA modules
• Measures and generalizations of dual Littlewood identities
• Representations of Smith algebras which are free over the Cartan subalgebra
• A class of non-weight modules over the super-BMS${}_3$ algebra
• Non-weight representations of Cartan type S Lie algebras
• Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$
• Simple $\mathfrak{sl}(V)$-modules which are free over an abelian subalgebra
• Representations of affine Nappi-Witten Lie algebras over polynomial algebras
• Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two
• Generalized Polynomial modules over the Virasoro algebra
• Exponentiation and Fourier transform of tensor modules of $\mathfrak{sl}(n+1)$
• Simple non-weight modules over Lie superalgebras of Block type
• The restriction of polynomial modules for the Virasoro algebra to $\mathfrak{sl}_2 ( \cc )$