New irreducible tensor product modules for the Virasoro algebra (II)

TL;DR

This paper constructs new irreducible Virasoro modules via tensor products of specific modules, providing criteria for irreducibility and isomorphism, and compares these with existing non-weight modules.

Contribution

It introduces a new class of irreducible Virasoro modules formed by tensor products and establishes conditions for their irreducibility and isomorphism, expanding the understanding of Virasoro representations.

Findings

Derived necessary and sufficient conditions for irreducibility.

Established criteria for module isomorphism.

Compared new modules with existing non-weight Virasoro modules.

Abstract

In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,\alpha,h)$ and $\Omega(\mu, b)$ with irreducible highest weight modules $V(\theta,h)$ or with irreducible Virasoro modules Ind$_{\theta}(N)$ defined in [MZ2]. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for two of them to be isomorphic. We also compare these modules with other known non-weight Virasoro modules.