Harish-Chandra modules over the $\Q$ Heisenberg-Virasoro Algebra

TL;DR

This paper classifies all irreducible Harish-Chandra modules over the $ ext{Q}$ Heisenberg-Virasoro algebra, showing they are all of intermediate series with one-dimensional weight spaces.

Contribution

It proves that every irreducible Harish-Chandra module over this algebra is of intermediate series, extending understanding of module structures in this algebraic context.

Findings

All irreducible Harish-Chandra modules are of intermediate series.

All such modules have one-dimensional weight spaces.

Complete classification of these modules is achieved.

Abstract

In this paper, it is proved that all irreducible Harish-Chandra modules over the $\Q$ Heisenberg-Virasoro algebra are of intermediate series (all weight spaces are 1-dimensional).