Verma modules over deformed generalized Heisenberg-Virasoro algebras

TL;DR

This paper investigates the structure of Verma modules over a class of deformed generalized Heisenberg-Virasoro algebras, providing a complete characterization of their irreducibility depending on algebra parameters.

Contribution

It introduces a new class of Verma modules over deformed algebras and completely characterizes their irreducibility conditions.

Findings

Complete irreducibility criteria for Verma modules over the algebra.

Identification of parameters affecting module reducibility.

Extension of representation theory for deformed generalized Heisenberg-Virasoro algebras.

Abstract

Let $\mathfrak g(G,\lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda\neq-1$ 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.