New irreducible non-weight Virasoro modules from tensor products

TL;DR

This paper constructs new irreducible non-weight Virasoro modules by tensoring specific modules, providing conditions for their irreducibility and isomorphism, and establishing their novelty in the field.

Contribution

It introduces a new class of irreducible non-weight Virasoro modules via tensor products and determines their irreducibility and isomorphism conditions.

Findings

Derived necessary and sufficient conditions for irreducibility.

Established criteria for module isomorphism.

Proved the modules in this class are new contributions.

Abstract

In this paper, we present a class of non-weight Virasoro modules $\mathcal{M}\big(V,\Omega(\lambda_0,\alpha_0)\big)\otimes\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i)$ where $\Omega(\lambda_i,\alpha_i)$ and $\mathcal{M}\big(V,\Omega(\lambda_0,\alpha_0)\big)$ are irreducible Virasoro modules defined in \cite{LZ2} and \cite{LZ} respectively. The necessary and sufficient conditions for $\mathcal{M}\big(V,\Omega(\lambda_0,\alpha_0)\big)\otimes\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i)$ to be irreducible are obtained. Then we determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. At last, we show that the irreducible modules in this class are new.