2021/02/01 by Chen, Qiu-Fan, Yao, Yu-Feng
#17B10 #17B65 #17B68 #17B70 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2102.00979
In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A1 by taking tensor products of irreducibles defined in [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro algebra of type A1, 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 A1, and give sufficient and necessary conditions for these induced modules to be reducible.