English

Tensor product weight modules over the affine-Virasoro algebra

Representation Theory 2024-07-30 v1 Rings and Algebras

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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Cite

@article{arxiv.2407.19844,
  title  = {Tensor product weight modules over the affine-Virasoro algebra},
  author = {Qiu-Fan Chen and Yu-Feng Yao},
  journal= {arXiv preprint arXiv:2407.19844},
  year   = {2024}
}

Comments

23 pages

R2 v1 2026-06-28T17:56:37.398Z