A new class of irreducible modules over the affine-Virasoro algebra of type $A_1$

TL;DR

This paper introduces a new class of irreducible non-weight modules over the affine-Virasoro algebra of type A_1, constructed via tensor products, with conditions for irreducibility and isomorphism, expanding the known module landscape.

Contribution

It constructs and characterizes a novel class of irreducible modules over affine-Virasoro algebra of type A_1, including criteria for irreducibility and isomorphism, and demonstrates their novelty.

Findings

Established necessary and sufficient conditions for irreducibility.

Determined criteria for module isomorphism.

Showed these modules are new compared to existing ones.

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 a finite number of irreducible modules $M(\lambda, \alpha, \beta, \gamma)$ with irreducible highest weight modules $V(\eta, \epsilon, \theta)$. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for such two modules to be isomorphic. We also compare these modules with other known non-weight modules, showing that these irreducible modules are new.