Tensor product of generalized polynomial modules for the Virasoro algebra (Q6612147)

The Virasoro algebra is one of the most important infinite-dimensional Lie algebra both in mathematics and mathematical physics. The representation theory plays a crucial role in theoretical physics and other mathematical branches, i.e., quantum physics, conformal field theory, and vertex operator algebras. The present authors construct a class of modules over the Virasoro algebra by taking tensor products of certain modules. This provides a unified description of many known examples of Virasoro modules. The authors obtain the necessary and sufficient conditions for the class of modules to be irreducible and study their submodule structure when they are reducible. They also determine the conditions for two such modules to be isomorphic. In the last part of the paper, they compare the tensor product modules with other known Virasoro modules, concluding that they provide new simple modules in general.