Verma modules over deformed generalized Heisenberg-Virasoro algebras

Abstract

Let $\mathfrak{g}(G,\lambda )$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda \ne -1$ and an additive subgroup $G$ of $\mathbb{C}$. For a total order on $G$ that is compatible with addition, a Verma module over $\mathfrak{g}(G,\lambda )$ is defined. In this paper, we completely determine the irreducibility of these Verma modules.

11 pages