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The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang [Z] in 1997.
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V. Mazorchuk and K. Zhao, Classification of simple weight Virasoro modules with a finite-dimensional weight space, J. Algebra
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G. Liu, R. Lü and K. Zhao, A class of simple weight Virasoro modules, Preprint, arXiv:1211.0998
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2012
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