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arXiv · 2407.19844

Tensor product weight modules over the affine-Virasoro algebra

Qiu-Fan Chen·Yu-Feng Yao
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Abstract

In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo, K. Zhao, Tensor product weight modules over the Virasoro algebra, J. Lond. Math. Soc. 88(2013), 829-844.]. All such tensor product modules are indecomposable modules with infinite-dimensional weight spaces. Moreover, we obtain the necessary and sufficient conditions for such tensor product modules to be irreducible. Therefore, we obtain a class of new irreducible weight modules over the affine-Virasoro algebra. Finally, the necessary and sufficient conditions for any two such tensor product modules to be isomorphic are also determined.

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Qiu-Fan Chen, Yu-Feng Yao. 2024-07-29. Tensor product weight modules over the affine-Virasoro algebra. https://arxiv.org/abs/2407.19844

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