Verma modules over deformed generalized Heisenberg-Virasoro algebras (Q2031519)

In the present paper, the author study the Verma module over the deformed generalized Heisenberg-Virasoro algebra \(\mathfrak{g}(G,\lambda)\) with \(\lambda\neq-1\), which are generalizations of the Heisenberg-Virasoro algebra, deformed Heisenberg-Virasoro algebras and generalized Heisenberg-Virasoro algebras. A complete description of the irreducibility of the Verma modules over \(\mathfrak{g}(G,\lambda)\) in both cases where the total order on \(G\) is dense and discrete is given. Particularly, the irreducibility of the Verma modules over \(\mathfrak{g}(G,\lambda)\) is completely determined for the discrete order case of \(G\).