Irreducible tensor product modules over the affine-Virasoro algebra of type A₁

Abstract

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking the tensor product of irreducible $U(\mathfrak{h})$-free modules of rank 1 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.

Keywords:

• Affine-Virasoro algebra
• tensor product
• non-weight module
• highest weight module

2020 Mathematics Subject Classifications:

• 17B10
• 17B65
• 17B68
• 17B70

Acknowledgments

Yu-Feng Yao is grateful to professor Yufeng Pei for providing the references [1, 7].

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 12271345 and 12071136].