Irreducible Virasoro modules from irreducible Weyl modules

Abstract

We use Block's results to classify irreducible modules over the differential operator algebra $\mathbb{C}[t,t^{-1},\frac{d}{dt}]$. From this classification and using "the twisting technique" we construct a lot of new irreducible modules over the Virasoro algebra. These new irreducible Virasoro modules are generally not weight modules. We determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. Many examples for such irreducible Virasoro modules with different features are provided at the end of the paper. In particular the class of irreducible Virasoro modules $\Omega (\lambda ,b)$ are defined on the polynomial algebra $\mathbb{C}[x]$.

16 pages

References in corpus (5)

• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• Irreducible Virasoro modules from tensor products
• A family of simple weight modules over the Virasoro algebra
• Whittaker categories for the Virasoro algebra
• Simple Virasoro modules induced from codimension one subalgebras of the positive part

Cited by in corpus (4)

• A family of simple weight modules over the Virasoro algebra
• Irreducible modules over Witt algebras ${\mathcal{W}}_n$ and over ${\mathfrak{sl}}_{n+1}(\mathbb{C})$
• $\W_n^+$- and $W_n$-module structures on $U(h)$
• A class of simple weight Virasoro modules