Abstract
In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules with irreducible highest weight modules or with irreducible Virasoro modules defined in Mazorchuk and Zhao (Selecta Math. (N.S.) 20:839–854, 2014). We determine the necessary and sufficient conditions for two such irreducible tensor products to be isomorphic. Then we prove that the tensor product of with a classical Whittaker module is isomorphic to the module defined in Mazorchuk and Weisner (Proc. Amer. Math. Soc. 142:3695–3703, 2014). As a by-product we obtain the necessary and sufficient conditions for the module to be irreducible. We also generalize the module to for any non-negative integer and use the above results to completely determine when the modules are irreducible. The submodules of are studied and an open problem in Guo et al. (J. Algebra 387:68–86, 2013) is solved. Feigin–Fuchs’ Theorem on singular vectors of Verma modules over the Virasoro algebra is crucial to our proofs in this paper.
Citation
Haijun Tan. Kaiming Zhao. "Irreducible Virasoro modules from tensor products." Ark. Mat. 54 (1) 181 - 200, April 2016. https://doi.org/10.1007/s11512-015-0222-2