A Family of Non-weight Modules over the Virasoro Algebra

In this paper, we consider the tensor product modules of a class of non-weight modules and highest weight modules over the Virasoro algebra. We determine the necessary and sufficient conditions for such modules to be simple and the isomorphism classes among all these modules. Finally, we prove that these simple non-weight modules are new if the highest weight module over the Virasoro algebra is non-trivial.

Modules for loop Affine-Virasoro algebras

In this paper, we study the representations of loop Affine-Virasoro algebras. As they have canonical triangular decomposition, we define Verma modules and their irreducible quotients. We give necessary and sufficient condition for a irreducible highest weight module to have finite dimensional weight spaces. We prove that an irreducible integrable module is either a highest weight module or a lowest weight module whenever the canonical central element acts non-trivially. At the end, we construct Affine central operators for each integer and they commute with the action of the Affine Lie algebra.

Irreducible Weight Modules with a Finite-Dimensional Weight Space over the Twisted N = 1 Schrödinger-Neveu-Schwarz Algebra

It is shown that there are no simple mixed modules over the twisted N = 1 Schrödinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a non-trivial finite-dimensional weight space is a Harish-Chandra module.

Duflo theorem for a class of generalized Weyl algebras

For a special class of generalized Weyl algebras (GWAs), we prove a Duflo theorem stating that the annihilator of any simple module is in fact the annihilator of a simple highest weight module.