Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$

TL;DR

This paper constructs and classifies new non-weight modules over the affine-Virasoro algebra of type A_1 using tensor products, demonstrating their novelty and providing conditions for their reducibility.

Contribution

It introduces a new class of non-weight modules via tensor products and characterizes their irreducibility and isomorphism classes, expanding the understanding of modules over affine-Virasoro algebras.

Findings

Constructed non-weight modules as tensor products

Determined irreducibility and isomorphism classes

Established conditions for reducibility of induced modules

Abstract

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of irreducibles defined in [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro algebra of type $A_1$, J. Math. Phys. 60, 071707 (2019)] with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type $A_1$, and give sufficient and necessary conditions for these induced modules to be reducible.