A family of simple weight modules over the Virasoro algebra

Abstract

Using simple modules over the derivation Lie algebra $C[t]\frac{d}{dt}$ of the associative polynomial algebra $C[t]$, we construct new weight Virasoro modules with all weight spaces infinite dimensional. We determine necessary and sufficient conditions for these new weight Virasoro modules to be simple, and determine necessary and sufficient conditions for two such weight Virasoro modules to be isomorphic. If such a weight Virasoro module is not simple, we obtain all its submodules. In particular, we completely determine the simplicity and the isomorphism classes of the weight modules defined in [C. Conley, C. Martin; A family of irreducible representations of the Witt Lie algebra with infinite-dimensional weight spaces. Compos. Math., 128(2), 153-175(2001)] which are a small portion of the modules constructed in this paper.

24 pages

References in corpus (7)

• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• Irreducible Virasoro modules from tensor products
• Irreducible Virasoro modules from irreducible Weyl modules
• Simple Virasoro modules induced from codimension one subalgebras of the positive part
• Whittaker categories for the Virasoro algebra
• Simple Virasoro modules which are locally finite over a positive part
• A class of simple weight Virasoro modules

Cited by in corpus (6)

• Modules over the Heisenberg-Virasoro and $W(2,2)$ algebras
• Irreducible Virasoro modules from irreducible Weyl 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 $U(h)$
• New irreducible tensor product modules for the Virasoro algebra
• Generalized Polynomial modules over the Virasoro algebra