2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105004For any additive subgroup $G$ of an arbitrary field $F$ of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra $L[G]$. Given a total order of $G$ compatible with its group structure, and any $h,h_I,c,c_I,c_{LI}\in F$, a Verma module $M(h,h_I,c,c_I,c_{LI})$ over $L[G]$ is defined. In the this note, the irreducibility of Verma modules $M(h,h_I,c,c_I,c_{LI})$ is completely determined.LaTeX, 9 pagesQuantum AlgebraRepresentation Theory17B56; 17B68text